I am not sure I am following you on swapping the body over, because unless there is something radically different on the Innovation, I would have expected it to perform exactly the same as our Turbomaster. Our UK version of the Innovation performed exactly the same as the hardbag alternative, indeed with the exception of a bag-full indicator lamp, I can think of no other difference between the softbag cleaner and the standard hardbag model.
I think the reason the Turbomaster Softbag was so very unpopular in the UK was because it was on sale at a time where almost all uprights were of a hard-bag design, be it clean-fan or dirty-fan. What few softbag cleaners there were served only to fill two sectors of the market: the budget customer, and those who wanted something lightweight & basic. The Turbomaster fulfilled neither request, as it was not inexpensive to purchase, and it was physically heavy & loaded with features. From what I can ascertain of the USA market, your choice of softbag cleaners has always been vast for many a year, giving rise to a place for a model such at the Innovation. Over here it was completely surplus to requirement.