You can use much longer primers (up to 70bp or so), such that they span the repetitive region you want to change and some more specific sequence to anchor the primer (assuming your vector allows). If the multiple sites you want to change are within range of one another, you can order primers with 2 or more mutagenised sites - though expect your efficiency to drop. Your other option would be to do multiple rounds of mutagenesis, altering one position at a time.
I would then simply try these primers on a gradient PCR using a good enzyme like NEB's Q5. Trying to find a temperature for the correct size band will likely be key.
The real problem you're going to have though probably isn't the cloning, it'll be proving it. Homopolymer stretches are a real problem for sequencing, and the longer they get the worse it is. Automated sequencers find it difficult to tell between, for instance, 29 Adenines, and 30 adenines in a row. When your sequencing results are returned, if your sequencing is off by a base or two, it will be pretty much impossible to tell if your sequencing was wrong, or your construct was.