The problem is that no matter which way you cut it, it doesn’t totally work. Your solution on paper sounds like the best, but even if you cut out Anakin’s Skywalker name, there are a few too many hints - Padme’s pregnancy, Anakin’s being from Tatooine, the whole Lars homestead, and Anakin’s lightsaber (possibly the biggest one you can’t get around).
True, my edit won’t contain the tatooine part of AOTC, and with TPM being the most expendable installment in the series, you could avoid the tatooine problem by completely removing it in a hybrid edit. Padme’s pregnancy is pretty hard to get around, and Anakin’s lightsaber would pretty much need to get cut out and around as much as possible so that the audience never focuses on that hilt. That’s still a bit of a reach but I think it’s doable.