@steve@pkhuong@zwarich "Guess (and verify) the next quotient digit" sure works a lot better in base 10. Of course you can do binary search in base 2^n to guess more efficiently but that's effectively reducing to base 2, which is the ultimate cheat move.
Much later I found this technical note by Per Brinch-Hansen who has a stepwise discussion and development of how to do it. I believe he recommends (for tutorial purposes) a less tight estimate that can be off by 2 or 3 in the worst case.