Shouldn't tidal locking be impossible for a satellite that has a considerably eccentric orbit?
You are right, that would be weird if the Moon speeds up and slows down this way to always show the exact same side to the Earth. That's why it doesn't.
At some point in the orbit the Moon's rotation (its phase) lags behind and at some point it is too fast. It is (pretty much) constant and does not adjust to the varying orbital velocity. That's (one reason) why it wobbles. And this wobble is what's called libration.
But the Moon is still tidally locked as its rotation period is still equal to its orbital period.