3500W generator I picked up

I'm not sure that neutral is an issue. The neutral is tied to ground at the pole and at the house.
After reading much on this subject, I think I am going to just run a 10-3 30 amp rated cord into the house through the dog door,...
you probably would never of had an issue with what you first planned, but i'm glad you came up with a simpler solution. the electric company doesn't know who knows what they're doing and who's an idiot. i've spent enough time going to peoples houses when there's an outage, trying to figure out if they hooked up the genni correctly. if it was hooked into the panel without a visible open to the service, or a proper transfer switch, they had to disconnect it or we'd cut the service at the pole. they'd be the last ones on too