Damn! - the RFI filter trick didn't work for the furnace after all. Got around to building an official RFI filter in an electrical box, but it all together, and it didn't work! - flame sensor kicking out.
Back to the drawing board, running experiments, come to find out that is has something to do with "grounding" (as one poster mentioned). Took all the RFI crap out of the circuit, and just ran line/neutral from the Honda eu2000i, and let the ground float, and it all works fine. I have a cheater cord which is an old 2-prong cloths iron coard, with aligator clips on the other end. Plug that into the generator, and aligator clip to just line and neutral of the 3-prong plug on the furnace, and it works. Whats the dealy-O ? I don't imagine that I can tie neutral and ground together at the generator since its an inverter. Ain't that something. when I "thought" I got it to work with the RFI torroiods and such, I realized that I was testing all of that with my trusty 2-prong cheater cord (I love that thing). So when I thought I solved it with the RFI filter, I was doing it with the ground floating (which is all that it takes to make it work).
Back out to the bench with scope in hand, will let you know what I ultimately conclude.