Usually the ls trucks with the 4.8 don't have tranny coolers, and most don't have reciever hitches and trailer plugs, so if yours has all that your lucky.
Yes the gear change would help you greatly. A 3.73 or maybe a 4.10- if you tow alot. But if wanting factory gears this may set you back $1500+ per differential. The 3.23s you have just dont keep the truck up in the rpms to keep it in the power band.
I have a set of OE 4.10 gears in a tahoe diff. I could get rid of if your ever in the central ok area.
Best of luck!
MillerTime- Future Sabre Handler!!