I don't think you have anything to worry about spooling the 5.3 or the 4L60E to 6000 RPM ... The motor will handle 6200 or so ... The tranny is rated at 6100 Max ... The factory set fuel cut on the cable throttle av's is 5940 ...
The 5.3 valvetrain will not allow power much over 4900-5,000 or so, but winding it up is not detrimental at all providing you are good with preventative maintenance and checks ...
FYI, I see 4.8 liter manuals running at the track shifting at 6200 or so ... The LS1 derivatives are really the strongest chevy small block in history ... IMHO ... The only thing I have heard of being an issue is hitting full boost or the bottle off the line... It tends to spin the rear mains due to the weight of the truck... But having 6 bolts and a deep skirt block, they will last much longer under the abuse than a pre '96 Vortec 350 ... !!!
11H