Each turn, before you touch the jenga stack, you must start reciting a poem belonging to a canonical verse form.
The canon would include, let's say, limericks, haiku, double-dactyls and sonnets.
The poem can be from memory or a fresh composition, but you must complete your turn before the poem
Audience consensus will identify any excessive pausing, in which case the hesitant must take an extra turn (this being a disadvantage in jenga). A similar penalty will attend free verse.
An international final is contested between Cyrano de Bergerac and Hermione Granger. In the first rubber de Bergerac reaches a winning position, which he chivalrously throws away, felling the stack with a sweep of his nose. This patronizing gesture, accompanied by a cloying sonnet in a Peter Sellers French accent, annoys Granger so much that she loses her composure, the next two rounds and the title. The losing semi-finalists were a Swiss watch-maker and a Japanese flower-arranger, both minor characters from - let's say - something by Kazuo Ishiguro.
The great trick is that, the more intriguing the poem (and its presentation), the longer the pauses the audience will tolerate, because they will want to hear how it ends more than they will want to penalize the player.