I think I agree with the above post about using a modern chassis cut to fit. As for the older 350 engines they have plenty of power to pull your trailer. I guess the guy who said he didn't think they did wasn't around in the 60'70's when that was what we had and got by just fine. I think I'd perhaps go for a later model perhaps like a 96'+ to get the 5.3 Vortec and OD transmission. I've pulled heavily laden 2 axle trailers with that combination across the country with no sweat at all. Also you'll likely have to rewire the truck anyway so getting the computer circuitry from a donor is a no brainer and lots of people have done this swap so there's lots of good input both here and at Inliners & Chevytalk. This is likely to be the best and least expensive route in the long run plus you'll get PS and PB in the deal so there is all you've asked for;
Drivability, dependability, economy, safety and performance. Good Luck and be sure to keep us posted with lots of photos and Welcome Aboard.