My wife has never complained about the wireless remote. She just pushes the button and varoom. Coffee, dry hair, ac and popcorn.
What size ac do you have? My 3000 Honda runs a 13,500 just fine with eco OFF, with eco on it hits hard sometimes with compressor start up.
On one hand I'd say get the 3400 but someone who owns those models can tell you more. You'd sure think the 3100 would be fine
Our Genny is bolted in the truck bed so we'd have to climb up there to start it. How you use yours would also make a difference in needing the remote. We use ours for 7 months at a time so it's a daily thing