Thanks to all who have replied.
As we are having a very difficult time finding a Suburban (or Express Van) with a 6.0, based on most of your experiences, we are going to consider a 1500 Suburban with the 5.3 (btw-been towing with 1/2 tons for years so not afraid of them. The '65 Van is a 1/2 ton and has towed with no breakdowns and safely for 90,000 miles). I really want the 3.73 gears, but how can you tell if it has them? Most owners have no idea and some don't even know what engine they have.
The other thing is that I can't seem to find out on the internet what, for example, an '03 1500 Suburban weighs? The Envoy weighs 5000 lbs which really shocked me cause its so small (compared to a Suburban). So if the Suburban weighs about that much then the 5.3 should do the job nicely since the Envoy's 4.2 does ok, mainly we want more interior room.
My ideal Suburban would be a 5.3, 3.73, 2wd, stripped down model with cloth seats, with 150,000 miles or less (hate leather).