I think there will be a lot of Class B vans that can tow that weight.
I've put the data from my van into towing calculators and think 3600 lbs or so would be OK for my van.
I suggest looking for a van with an external transmission cooler and a 4.10 rear axle ratio. The '04 Chevy based Roadtrek I owned had both. I'm not that up-to-date on used Class B pricing but think your budget should be enough to buy something like that.
My current van has a 3.73 rear axle ratio and that was a factor in settling on the 3600 lbs tow weight for it.
This topic has some good info: http://www.classbforum.com/phpBB2/vi....php?f=9&t=615
I towed a car behind my Class C. Your setup would be a bit different if you use a dolly. I towed the SUV with 4 wheels on the ground (no dolly).