Endless Checkout Progress Bar (Yes, again)

As described in two closed forum posts, installing Free Order causes my checkout payment progress bar to scroll endlessly. Two previous patches have fixed this in some circumstances. I have checked the module files, and both of those patches are now included in 6.x-1.0-beta4. So this is something new. This happens with and without other payment methods being installed. I don't have a clue what's causing it.