I agree with ssobol. The 1100 BTU is not a lot of cooling. But the BTU is not the whole story--we don't know what the cu. foot per min output is. you could use fans in the V berth area to circulate the air.
I suspect if you fully insulted the forward cabin, including a "door" (could be bubble foil or foil covered styrofoam "sheets", that you probably could get that area to 20* below outside ambient temp. You would have to have a bucket for the condensate (you could collect the water for washing dishes etc). Plus the "hose" has to go out an open window, to get rid of the heat removed from the air.
We used the 5,000 BTU window unit on our25, blowing into the cabin, where the outside was about 105, and got the cabin (with bubble mylar insulation on the windows) down to 85 degrees--certainly more comfortable. The 22, you can get a little lower.
There have been several boaters who have used the window units, with ducting to blow cold air under a jacket to cool their body when at the helm...
Some of the photos on the web site are ridiculous. Sitting out of doors, and blowing on a group of folks on a pontoon boat for example.
Living in Florida, we find the breeze is adequate during the day, but when in the 90's at night-sure nice to have AC.--or a really good breeze.
The 18650 battery is common enough--I use it in one of my portable radio receivers. (Tesla does use this battery in the current higher priced cars--The battery is 16mm diameter x 65 mm long. In the larger battery pack there are 7104 batteries, the smaller 5376 batteries. The new Series 3 is rumored to be using a new larger battery: 21mm diameter x 70 mm long).