Is there an advantage to the 1" sensor? Opinions requested.

Unless that teleconverter is very good, it might not be any better than cropping.  I have a couple of inexpensive TCs, and I don't think I ever decided if it was better with or without; I think in some cases it did seem better than cropping, but there was noticeable loss of detail, and it was harder to use (focus).  This is mostly with my DSLR, though.

--
Gary W.