I just picked up a 1998 Four Wheel Camper shell model, the plate says it weighs around 800 pounds. I'm using my 2006 4cylinder 5spd 4X4 Tacoma to haul it. On the trip home, with only a set of helper springs on the back, the truck rode fine but was sagged. I did not have any sway issues though. I've ordered an add a leaf and Timbrens for the rear and while I'm at it, I'm putting Timbrens on the front with a hitch. My plan is to throw a TW200 on the front sometimes, more often a bicycle rack. I was surprised at how well the truck handled the camper with only helper springs. I have owned a 2001 Tundra and I think if you did similar mods, add a leaf with Timbrens/airbags you shouldn't have a problem. The Timbrens on the front are designed for plows and such, so I think they will work find with a moto.
There really isn't much of a size difference from a first gen Tundra and the current gen Tacoma. Yes the Tundra is bigger but overall, they are similar. The pros to the Tundra are the V8 and starting out with a "half ton" rating. Suspension wise, they are almost identical to the Tacoma. I would just look out for Frame Rust depending on where you are looking to purchase. The Tundras of that gen were subject to the recall and many did get new frames.
Post pictures of your setup once you get there!!!
Cheers,
Jorge