Can multiple flight instructors work?
Well it works for the military so I’ll say yes.
Of course that is helped with strict standardization too, something not always present if training at a location, or multiple locations, without a syllabus.
Personally I don’t think you should have quit your job to do your initial training. You had no prior experience with flight and really have no idea if flying if for you. I’m not a fan of pilot-mill fast track programs for training or cost, but if are committed to this road and want quick training then they could get you the PPL in weeks verses months. You will not be retaining knowledge at the rate you are currently flying so every flight will be a refresher basically instead of moving forward.