When you say "strip off all the old paint", I wouldn't. If you're thinking of getting back to a natural wood finish, pretty tough
I agree- Unless the builder did a perfect job on the fill coats, it's going to be difficult not to have pinpoints of paint left behind, even if you use a chemical stripper. And, as Jay mentions, the repair will be visible in any case.
I'd pick a different paint scheme and just paint over the existing paint.