Don't forget the fusing on the DC side. 2000W is about 166A or a 200A fuse or so. Type T is best, but a MRBF is probably good enough. Or is that the round thing?
From the
wiring calculator 2/0 wire will get you to around 25' R/T, but I'd guess you know that.
If it's still a consideration, we get by just fine with our 1000W inverter, but then we don't use the microwave hardly at all even when plugged in. That would reduce the wire quite a bit. AS has 4AWG going to our inverter.
Last, I'd look into some sort of relay to automatically switch off the charger in case you forget. I'm pretty sure they exist but I haven't had the occasion to research them.