PE is the resident expert on this area of color processing.
I have found that you absolutely need a stop bath between the developer and blix. I had similar and worse problems without it.
I can't see any reason why a low pH fixer wouldn't work before the blix, but I haven't tried it. The most likely horror scenario would probably be some sort of color shift. The usual order for separate bleach and fix (which does work) is to bleach first, but that is because silver salts are created by bleaching, and they need to be fixed out. You are trying to just ease the fixing burden of the blix by getting rid of the undeveloped silver first so that all the fixer in the blix has to do is remove the bleached silver salts. Sounds reasonable.
As has been noted here before, blix is a terribly unstable mixture. The bleaching agent and fixing agent attack each other, and the combination doesn't last long. It is a situation somewhat like Farmer's reducer. In any case, time as well as capacity is a real issue with blix. Once it is mixed, it goes bad after a day or two.