I'm stupid, I guess. I saw the last slide ("there is no problem as the system is still running" (and chmod can therefore still be executed)) and thought that was the solution.
Once again I've learned that for every problem there is a solution that is clear, simple and wrong (and that I myself am quite likely to hit upon this solution).
If you try it, you'll find that it doesn't, in fact, work. Apparently the shell performs a lookup of the access rights of the program you're trying to execute, meaning once you've done "chmod -x chmod", you really have created yourself a problem.
I'd now say the solution is something like this:
cp -pr /bin/chown /bin/chown.safe
cp /bin/chmod /bin/chown
chown 755/bin/chmod
cp /bin/chown.safe /bin/chown
[edit: formatting]