Most would agree that timing is vital to the comedians in Edinburgh this summer. But, this year, it has also proven crucial for political dramatists.

For the past two festivals, Scotland has known exactly where it was in the legislative diary. The 2014 fringe was full of plays about what it would mean if Scotland voted to leave the UK, while the 2015 listings were filled with reflections on the consequences of the remain vote.

But, when the scripts for this year were being written, the laptop screen in front of a playwright was a cloudy crystal ball. As the official fringe programme went to press in the spring, the EU referendum was still weeks away, it was not yet certain that Donald Trump and Hillary Clinton would be the US presidential nominees, and it was commonly held that Jeremy Corbyn was unlikely to still be leading the Labour party by the summer.

So a political writer needed to be either extremely brave or prophetic. The stand-up comics, well used to the necessity of topicality, have been able to adjust. The journalist-performer Viv Groskop’s show, Be More Margo (Stand 3 & 4), now has “Post-Brexit Edition” stamped across the posters , its theme of social climbing having been tweaked for Theresa May’s Britain.

Occupying even more scorched earth, Bridget Christie – whose 11am gigs at the Stand comedy club have become an Edinburgh must-see; this week’s returns queue was almost as long the one for the ticketed – has kept the title, Mortal, of her planned show about facing up to death. The content, however, has had an emergency reworking. Anecdotes about her potted fuchsias become metaphors for xenophobia, culminating in two of Christie’s signature turbo-riffs, when the pace and weight of words seems to threaten her with asphyxia, about Nigel Farage and Michael Gove.

Plays, however, are harder to change. There seem to be more cancelled productions than usual this year, including Party Time, an advertised drama about a politician suffering meltdown in a TV interview. And, although no-shows can be due to logistical or economic reasons, it was tempting to wonder, walking round the city this week, if the lengths of gaffer tape obscuring now empty time-slots outside venues covered up time-expired dramas such as Cameron Remains, Angela Eagle Takes Off!, Governor Scott Walker for President and A Night With John Whittingdale.

One gamble with history that has paid off is the return of one of last year’s hits, David Benson’s portrayal of the cabinet’s only surviving Old Etonian in Tom Crawshaw’s play Boris: World King (Pleasance Dome). There must have been a moment on 30 June, after BoJo’s withdrawal from the leadership race, when Benson and Crawshaw feared they were sending a white (haired) elephant to Edinburgh. But the politician’s unexpected resurrection at the Foreign Office means Boris has instead more or less achieved the show’s subtitle.

Benson, under a blond dish-mop wig, has verbally and physically perfected his portrayal of the politician’s ruthlessly calculated spontaneity, and a daring tonal shift in the script – a furious moral interlude in which the audience is warned that Johnson may not be as harmless as his rumpled buffoonery suggests – has even more force when aimed at the holder of one of the great offices of state.

Another presentation that has benefited from a change in context is Mrs Roosevelt Flies to London (Assembly Hall). Written and performed by Alison Skilbeck, this monologue about the former first lady’s morale-raising trip to the UK in 1942 has had a previous life, and was always a moving and bravura performance. But with the advance on the White House of Hillary Clinton, who has admitted to having imaginary conversations with Eleanor Roosevelt about women in politics, the show has gained an extra resonance. References to the compromises of political marriage and the different public attitudes to male and female ambition now look sharply forwards as well as back.

There is a more direct treatment of the Democratic nominee in On The Conditions and Possibilities of Hillary Clinton Taking Me as Her Young Lover (Summerhall), a bizarrely entertaining lunchtime show in which the New Zealand comedian Arthur Meek plays a disturbed academic who gives the audience a PowerPoint presentation on the historical and psephological reasons that he should as a male Monica Lewinsky to the second President Clinton. Both Mrs Clinton and Roosevelt might enjoy the subtext of double standards applied to the sexuality of female politicians, but, if things go Hillary’s way in November, it is unlikely Meek will be invited to perform at the inauguration.

Meek has a good gag about having been offered a slot at the venue “between the morning puppet show and the afternoon puppet show”. And, presumably encouraged by the popularity of mannequins across the theatrical spectrum – from the experimental (Kneehigh) to the mainstream (War Horse) – even Punch and Judy would find it hard to dispute that many of this year’s stand-out performers are attached to a string, have a hand up their bottom or a mask on their face.

Masked hits include Finding Joy (Assembly Hall), Vamos Theatre’s wordless work about a teenager caring for a granny with dementia, while adult puppet shows include an Australian import, Randy Writes a Novel, in which a soft toy protagonist, who has clearly seen Avenue Q, suffers a creative breakdown.

There is also a trend for lollipop masks, in which actors or audience members hold up a cardboard or hardboard oval with the photo of a face to cover their own. These are used in Mark Thomas’s political memoir The Red Shed (Traverse), and The Chicken Trial (Pleasance Courtyard), a fascinating Finnish drama based on the real case of a Swedish art student put on trial for animal cruelty after an installation involving the admission of hens to a nightclub.

One advantage of masks and puppets is they make casts look larger, usefully addressing the problem that budgetary economics increasingly make the monologue or solo show the default Edinburgh format.

This doesn’t matter if the entertainer is as multi-voiced and talented as Vivienne Acheampong, an actor who draws on her experience as a primary school-teacher in the crowd-funded Rainbow Class (Assembly Hall). With astonishing vocal versatility, Acheampong embodies a school full of characters including the Australian headteacher, Northern Irish deputy, a Ukip-leaning “midday supervisor” (dinnerlady) and assorted pupils with a variety of statemented conditions. The audience are variously parents and pupils. Even though I spent part of the performance on the ‘naughty chair’ in the corner of the classroom – after misbehaving during a recorder lesson – I can give Miss Acheampong an A+ report for this verbal extravaganza.

Another powerful demonstration of how a single performer can have the punch of a large cast is Angel (Gilded Balloon), in which Filipa Bragança indelibly portrays the ‘Angel of Kobane’, a young Kurdish woman called Rehana who is reputed to have shot 100 Islamic State fighters in Syria. Playwright Henry Naylor won awards for his last two fringe shows, The Collector and Echoes, which explored other aspects of Middle East politics; he has surely delivered another hit here with a script that gives Rehana a credible back story and personality (complete with jokes and moments of fear) rather than making her a symbol of global tragedy.

Naylor has skirted the problem of writing about such fast-changing politics by taking a more distant geographical and chronological perspective. So too does this year’s most unlikely success, Iraq Out & Loud (Bob’s Blundabuss, Potterow), in which volunteers are voicing, day and night, all 2.6m words, footnotes and all, in the 10 volumes of Sir John Chilcot’s long-delayed report into the invasion of Iraq.

While luck can only be wished to those readers who are landed with the indices and appendices at the denouement, the sections I got (at 9.50am on Tuesday and 7.40am on Wednesday) from the first two volumes proved as chilling as any paperback thriller – coincidentally or not, it is in paragraph 666 that Blair seems to seal a devil’s deal over military intervention – and often even laugh out-loud funny. “Although there is no doubt that the president did say that,” General Colin Powell says at one point, “it was not what he intended to say.”

With the events described in the Chilcot report having happened nearly 15 years ago, the show seems a fitting hit for a fringe that has had – due to uncertainties in Westminster, Holyrood and Washington – to be canny with its timing.

Three to see

Angel (Gilded Balloon) – Dramatist Henry Naylor and performer Filipa Bragança create an emotionally shattering account of the life of a young female Kurdish freedom fighter.

My Eyes Went Dark (Traverse) – Cal MacAninch gives one powerful
performance and Thusitha Jayasundera several more in Matthew Wilkinson’s
revenge tragedy about an man trying to nail those to blame for his
family’s death.

Rainbow Class (Assembly Hall) – Former schoolteacher Vivienne
Acheampong shows supernatural vocal versatility in bringing staff,
students and parents of a troubled London primary to life