Can I use an EZ Generator Switch as a transfer switch with a Generac GB1000 battery and a gas furnace (Bryant 340aav). If so, should it be setup as bonded neutral or floating neutral (I'm guessing it's supposed to be floating neutral). If not, is there a transfer switch that would work? (maybe Reliance Controls?)
Yes, the EZ Generator Switch is perfectly usable and uniquely suited for furnaces - pretty much the "killer app" for that particular product.
Your furnace will already have a steel Handy-Box containing a switch and/or fuse. You simply replace the Handy-Box with - well, follow the instructions.
The only thing I don't like is the need to leave door cracked open for the extension cord, since carbon monox.... battery, duh, nevermind!
Honestly, I'm not sure the battery is going to work for you. These "solar generators" or "portable power stations" or whatever they call them these days, are biblically overpriced for what you get. You can tell they're scammy because you have to dig deep in the specs for The Single Most Important Parameter for these units that should be right up front. But they really, really do not want you to be a competent shopper, because if you were, you probably wouldn't buy one. At least not theirs lol.
As it happens the "1000" unit is 1000 Watt-Hours, and the "2000" unit is 2000 watt-hours. (Well OK it's in the model number, but you can't take that for granted, ever!) 1000 watt-hours is about the storage you can expect from a $150 car battery (better: deep cycle marine starting battery) from CostCo. And so you can rely on data from people who have tried running their furnace off a car battery, like this guy.
I don't agree with the hatchet job the guy did wiring up the furnace - it doesn't switch neutral like it needs to, and I don't see a fuse.
That video's report of 6 hours feels about right to me. Furnaces take a lot of power. Once you install the switch, switch it to generator and feed your furnace through an extension cord via a wall outlet and a Kill-A-Watt. It will read out the watts it is using.
Mind you, this only works because it's a gas furnace, and it's only using electricity to push the fluid around (e.g. air, or water in a hydronic system). A furnace that uses electricity as the literal heat source simply will not work on battery.
The cost of lithium batteries has dropped like a stone in the last 10 years, to 15 cents a watt-hour. The "power stations" haven't dropped a nickel and are still at $1 a watt-hour. I do not like them, I think they are insanely oversold to 1%ers and dumb people, and 99% of buyers think they will do more than they will do, because they don't understand amps and watts and watt-hours.