Is there anything I can do to up the tow rating of my Yuk? Even if not officially, is there anything I can do to make it more tow-capable? Suspension upgrades?
Short answer? No.
Longish answer: The limiting factor in your tow rating isn't the engine. It's the frame, brakes and axles. And again, that rear axle is the weak link. My buddy now owns my '01 half-ton, and it's wearing rear axle number four precisely because I blew up the first three towing heavy over long distances. Also the reason why I have a 2500 now.
And make sure you check your glove box code sticker to check your rear axle ratio. It's likely you have the 3.42, but you might have the 3.08 "soccer mom" axles, which significantly reduce your towing rating. I don't know the codes off the top of my head, but if the engine spins right at 2000 RPM at 80 MPH, you have the 3.42.
And regards to the engine revving high when towing on long grades? Well, of course it does. For maximum power, you want to keep your revs between the torque and horsepower peaks. The torque peak on the 6.2 is 4300 RPM, and the horsepower peak is 5700 RPM. Floor the pedal and hold it there, and it will surely settle in to that range.
Here's the picture I love to share - my dash, approaching the Eisenhower Tunnel in Colorado on I-70, the "Ike Gauntlet," over 10,000 feet in elevation, rig weight just over 16,000 lbs. Didn't have the pedal floored, but it seemed happy right around 4k. These motors love to rev - let the big dog eat!
PS - can anyone tell me why there's no "red line" on the tach?