Decisive points.

As you have shown them to not be equivalent, I would have done better to say:

"You can do what you should do" entails "You should do what you should do".

But if the latter statement is truly a tautology, that obviously doesn't help. If I then add your second edit, that by "should" I mean "provided one is able to", I am at least less wrong...but can my argument avoid being wrong only by being vacuous?

I think so.