I don't have the Honda 2000, but even with my Powerhouse PH4000Ri/E, I had issues with it stalling when my AC compressor started. I installed one of these EasyStart devices, and my generator barely even notices when the compressor starts now. I used to have to shut everything else off when the AC started, and now I can easily have other things running (other than the microwave). I was a little hesitant to spend the $300+ too, but I'm glad I did. I've heard that it can work with the Honda, and judging by my experience, I wouldn't doubt that. I was even able to get my AC to start running off a 20A outlet! I contacted their tech support before buying, and they drew me a wiring diagram specific to my unit. After that, it was super easy to install - just needed some quick disconnect terminals and a splice (and somewhere to mount the unit). Then just follow the directions and start your AC 5 times when plugged into shore power.
2016 Coachmen Freedom Express 282BHDS
2008 Dodge Ram 1500 QC 4x4 Big Horn, 5.7L HEMI