Weirdly, I get to answer my own question (in a way)!
I am in a band, and the bass player/singer has decided to do a weird version of Mack the Knife where he modulates up EVERY SINGLE VERSE for about six verses or more (if you count solos)! Crazy, I know, but that's what he wants to do...
Even though it's real band, the procedure and timing is the same. I hit the transpose a bar BEFORE the new verse, play a ii-V in the old key, but it comes out as the lead to the new key. Works pretty well, but if he goes crazy and does more than five key changes, I have to eventually modulate (my G70 will only go up 5 half steps).
If he keeps doing more than that on a regular basis, I might start to transpose DOWN a few steps before we start, and play in a higher key, and that will give me more steps before I run out of keys!
It's not something I usually do, but it stops this one getting completely crazy. Doesn't help with things like Down in Brazil, by Michael Franks, which is basically a cycle of ii-V's through the entire twelve keys, though!