Or ..... the OP can indeed pick up a 1000W genny and replace their non-power-factor-corrected converter/charger with a power-factor-corrected converter/charger.
There's a real place in the RV world for the more efficient PF corrected battery charging, but it's not talked about much - instead most RV campers just buy a bigger generator.
Here's a neat little PF corrected multi-stage charger that should easily work at full power from a quiet 1000W genny:
http://www.bestconverter.com/804-1240-02-Truecharge2-40-Amp_p_315.htmlOr maybe just the right 1000W genny would even run this slightly higher amperage charger at full power for even faster charging:
http://www.bestconverter.com/804-1260-02-Truecharge2-60-Amp_p_408.htmlBoth of the above RV chargers are also temperature compensated, so in moderate to warm weather their voltages are folded back and hence load any given small generator a bit less.