Correct Tow Vehicle Question for TM Models

We are seriously considering buying a TM and are looking for available used ones. We originally thought about a 2720 because of its light weight but the larger ones are so much nicer and we would like to consider them. We will be towing with a 2000 Chevy Astro van with towing package. The owners manual says we can tow up to 5300 to 5800 lbs (depending on our axle differential(?) which I don't know what it is). This of course includes cargo and extra passengers beyond two. Does anybody have experience or know about towing a 3023 or larger TM? Also, would we need a stabilizer hitch?