hi tpeltan, welcome to T'ville.
Actually I saw your post in my inbox before you deleted it - and it made perfect sense. If you backcross to one of the parents, or to a sibling in the same line, you're still moving towards stability. indeed, more homozygous genes is bound to result.
It does get a little tricky to reckon, just when will it be completely stable.
maybe seven generations is a good bet, whether you backcross or not. At least for us amateurs.