DHW no worries. I will be around. The hard start kit that I offer and use is the Supco SPP4E. It is the perfect size for this particular usage.
JCDriller. I fat handed the model number above so have corrected it. It is labeled as Artic Wind King.
Artic King amazon link.
As for which generator, I would suggest to go with the new Honda 2200i. Same frame size as the older EU2000i but now with more wattage. I say go with the 2kw only because should you purchase the smaller one, you are limited to a 1k watts. You open up your options with a little more weight, a bit more fuel consumption, slightly larger footprint but have the added power in your hands.
As for run time, you should get 6 to 8 hrs of run time but that will depend on load conditions. I have a 6 gallon marine tank connected to our Honda 2kw using an extended use gas cap and I swear it will run for 3 full days on that.
I have been working to construct a wired remote thermostat and an insulation pack. Being able to keep these at a DIY level remains to be seen as well as keeping the costs down. The remote thermostat currently is using a small PLC temp controller and replaces the window unit t-stat. Basically taking the units stat out of the control loop. The once turn knob on the front of the a/c unit then becomes a programmable controller with a 10ft lead. Possibly with a USB charging port. We shall see what comes out of it as I don't want to just use
As for the insulation pack....since the adapter can sweat (humidity dependent), this pack would alleviate most of this and would reduce some of the heat loss adding more BTU's to the ducting. I would offer this for those interested but it is very easy to make by end user. It is made simply by cutting some Reflectix to fit the three sides of the adapter. Simply spray glue them on and done. I am working with someone currently on making a one piece, sewn slip on cover. Should this yield good results, I will fully offer this as a option. The sewn on option will reduce the chance of damage since it can be removed by separating the Velcro. See pic for the Reflectix cut to fit.
Again, trying to keep it as DIY and affordable for the end user...choosing your ducting, power supply, paint colour or what. For those that want a turn key unit, feel free to contact me. Or if you want just and adapter, makes no difference to me.