They can pick a bit or two per page to attack, but then they're stuck with those bits.

In theory they could attack a new bit every few minutes, but that requires a system that allows the victim page to be remapped multiple times. KSM does not; any other memory-merging system could work the same way to mitigate things.

Even if they could keep remapping, it's a very slow attack that way. Reloading the checksum every ten minutes would keep you safe.