I was just using my Instax Wide 210 camera this week, and after using up a pack of film, kept the cartridge for possible future experimentation.
My initial thought is that the whole Instax cartridge is very precisely and elegantly made, for being something that is essentially thrown out after one use. I suspect one aspect of your processing problem could be the dimensional tolerances of your manual processing method. I would recommend an absolutely uniform pinching of the film pod between two metal rollers that are very precisely machined and also aligned very precisely so as to be parallel to each other, with the proper gap between them for ensure adequate pinching of the chemical pod.
An "easy" way to do this might be to employ a 4x5 Polaroid back, that already has the rollers in place, and figure out how to get the Instax film through it as a manual processor.