SoCalDesertRider wrote:
It is perfectly ok for the engine to run 4000 rpm pulling hills. If the tranny is hunting between gears, drop it down one manually so it stays there instead of shifting back and forth.
^^^^^ This one!
Correct - you can run at high RPM in GM trucks for miles and miles - just watch the engine heat gauge if you travel in hot weather. That's an indicator that the engine is working too hard.
But, I've been running GM 5.3 and 6.0 at high RPM for years in the mountains and never have problems. Your truck is a little under-powered and the gears are a bit high, but that means little beyond pulling slower in hill country. Just take your time and let the truck do its job.
If you ever change your truck, that would be the time to adjust the rear end ratio, and maybe the engine. But I would not worry about it for now.