With your current tow rig, options are very limited. Something like a Hunter Compact Jr might work. The Hunter Jr is usually the lightest F/G trailer out there, or really close to it. The Burro
13 sometimes is close too. There is a spreadsheet with actual tongue weight
and trailer weights. Advertised manufacturer weights are always ridiculously lower than real world weights.
Getting a trailer light
enough it can be towed with a Forrester will make living in it three months a challenge, BUT, we met a couple that were full timing in a Trillium
1300, no bathroom, no air conditioning
, very small, and they loved it (and had been doing it for two years!). (The Trillium
1300 will exceed your tongue weight limit).
Basically, within your figures, you are not going to get a bathroom and you are not going to get an air conditioner.
On the super light weight end of the spectrum, I was going to pull a Bunkhouse pop-up camper behind my Element. The Bunkhouse is meant to be pulled behind a motorcycle, weighs in at about 300 pounds with 40 pound tongue weight. It has a king sized bed and a 5x6 stand up area. OK for a weekend outing.
I ended up selling my Bunkhouse, so that plan is gone.
Here in NC, A/C is a must and I can't see three months full time without a bathroom. But people do it.
You may need to consider an SUV with more tow rating. There are plenty of them out there. Pay attention to tongue weight limit and payload, as you often will run out of those before you run out of tow rating. For example, my F150 has a tow rating of 9,800 pounds, but I run out of payload capacity at less than 5,000 pounds. And tongue weight is limited to 500 pounds too, a 9,800 pound trailer is going to have tongue weight of around 1100 pounds or more.
Tow ratings sell vehicles, but tongue weight and payload that are not mentioned often prevent it.
We all make mistakes, I've made some with several 000's on them for sure. The key is whether we can let go and move on. Sounds like you are there, which makes you a "winner". Losers feel they can't escape
and are "stuck".