I think you're plan is fine, except that a 20' TT is going to get awful small after a while. I've never owned a TT that small, can you get a full sized queen bed in one that you don't have to fold up every day? Shower will be small and very limited closet / storage space.
You might think you'll spend a lot of time outside so the little trailer will be fine. But if you're going to be there most of the year then you're going to spend more time inside to get out of the heat and humidity than you might expect.
If you buy new, see if you can get a 15K btu AC installed instead of the smaller one. With a slightly larger TT you might be able to get two ACs - what happens if one breaks down there? Make sure you get an awning also.
For off-grid the 20' TT may only come with one battery, you need at least two - again check on a slightly larger trailer. Four batteries would be ideal.
Bill