Yes, a jeep is pretty mundane at this time. I was thinking more towards an old FJ40 or even one of the old lifted Hilux pickups, thinking 5th or 6th gen (bonus points if you can find a 6th gen with crew cab). The mechanicals in those were pretty stout, frames.... dubious.

 

While miata is still always the answer, @paul has gone the Jeep & Toyota w/trailer, & 4wd sleeper van route. He DIY's his builds (he got the van new/gutted interior after a storage lot full of MB diesel 4wd vans destined for airstream got hail damage and sold for hilariously low prices...BDR included to make them look new) but you should be able to disappear $250k into some random line item no?

 

There are a few AWD Kei cars that can be had for a song, registerable, durable and JDMaf. Getting parts might be tricky but this sounds like a low duty cycle type of project.

https://carfromjapan.com/cheap-used-...5b58c1187cc0fe

 

There are also a lot of not-Kei JDM and ROW 4x4s that are pretty reasonable choices for a toad. Pajero JR, Land Cruiser Prado, etc. At the same price point I'd definitely go for the JDM over a Wrangler. I'd probably have gone that route if our toad wasn't also going to be my wife's DD. We ended up with a Grand Cherokee... much more civilized than a Wrangler on-road, but still has 90% of the off-road chops. It's also my wife's DD and she loves it. Probably bigger and heavier (5500lbs) than you're looking for, though.