Went through the same evaluation when I bought my EU2000 last summer. Check the charging output of your converter. Mine was only 3 amps--really only a trickle charge. I could get 8 amps from the generator 12v outlet, or I could plug in the battery charger which outputs up to 15 amps. So that's the way I went. I since have acquired a new camper with a better converter with higher output. I think I'll just plug the camper into the generator and let the converter do it. That's definitely the easiest thing to do.
We run 2 80aH batteries on the camper. Fairly conservative usage like you describe, and we can go up to 4 days without needing to recharge.
BTW, it's hard to justify the EU1000 when the EU2000 is just a couple of hundred bucks more. Keep in mind the output is reduced with altitude. The 2000 is a little bigger and definitely heavier, though.
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