The first algorithm in the paper where ratsimpmodprime was taken from should probably do quite well - as far as I can tell it shoud be about as fast as polynomial=True (maybe two or three times slower, or something of that order - not 100 times), and work quite well (it minimizes the maximum of the degrees of numerator and denominator). Will take a bit of work to implement, though (although it will nicely show of my commutative algebra module :D).
I implemented this in agca8 (no pull request, yet). It works, but I think its probably not very fast since my algorithms are not particularly optimized. When we push the trigsimp PR I will see how it goes with the other algorithm.
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