I mean you could make sure to limit couplings to 3rd cousins and beyond which eliminates like 99.5% of genetic problems for many generations,having an even more

I mean you could make sure to limit couplings to 3rd cousins and beyond which eliminates like 99.5% of genetic problems for many generations,having an even more diverse starting group also will help, and if you really wanted to make sure you could also send along some eggs and sperm to throw in the gene pool at times.