Thanks to wwest who gave the most concise reason as to why jumpering the neg to the ground on the inverter may not be the best idea. FYI, I completed my install yesterday, as per the manuals instructions, and all is well. Still not completely clear on the theory of grounding, but it is more of an academic issue than an implementation issue for me now.
As far as conflicts between the inverter/converter...I got around that the easy way - there is one dedicated line coming from the inverter. If there is anything I need to run, I'll plug it into that outlet. 600w is too small for the AC, microwave, toaster, coffee maker, etc. We've got workarounds for all those from our tent camping days, anyway. All of the systems seem to be happy running at 12v, except the TV, so that will be the primary use. Now I just have to manage the amps for best battery life....