GE version 3 works if I haven't already opened version 4 on the other computer (which, I assume sets the flag at Groundspeak for exceeding max views for the day). So Elliots4's observation appears to be spot on. I've reverted to version 3 everywhere, and seem to be OK.
So now I'm not sure that GE is blameless, since it was version 4 that that triggers the problem. And as long as they point the finger at Groundspeak and vice-versa, I doubt it will get fixed.