OP,
Please note that anyone of the few who had overheating with a 2004.5 or 2005 GM D/A LLY engine can make the fix for less than $100 to $150. It took a certain combination of circumstances to make them over heat. Pulling long grades near the max or over the max weight trailer at higher thinner air altitude on a very hot 95+ degree day with the pedal to the metal and then only a small percentage of the LLY's would overheat. The likelyhood of overheat with an LLY is very low and most by far have never seen it happen or come close to happening. There has been thread after thread on the many forums and only a few have complained about it while the vast majority of LLY owners had posted that it had never happened to their LLY. It was a vastly overblown possibility of occurrance mainly by loyalist blowhards of another brand of diesel pickup who didn't even own an LLY. You can search the various forums and see it clearly and in black and white on your own puter screen!
We have a Chevy 2004.5 D/A LLY and have pulled our 12,840 lb scale weighed 5th wheel with a 106 gallon, 100 gal usable filled aux diesel tank in the truck bed over the rockies several times in very hot summer temps and all over the smokies and the USA and Canada and never seen the temp over 210. Weight with the 5th wheel is 21,842 lbs scale weighed total rig weight with wife, our siberian husky. and I plus 2 boxes of tools on the back folded down seat of our crew cab long box 4X4. Normal engine temp is 190 and 260 is overheated per the truck's glove box manual. Our truck is total OEM as built under the hood and it's never had any repairs or needed any on the entire truck other than a couple burned out light bulbs, replaced the front brake pads at over 120,000 and they still had about 1/3 pad left, and tires of course. Truck will hit 150,000 on our way back home to Michigan from Florida where we are. The truck is only used for RVing with the 5th wheel or our 11'4" Lance truck camper on the back. We have other vehicles and are long retired so it's not a daily driver.
Injector problems were with the early LB7 engines Approx 2001-early 2003 which is before the LLY. GM extended the warranty on LB7 engines injectors to 7 years or 200,000 miles, which ever comes first. Most had already been replaced under warranty but some never needed it or were not done yet because of no problems with their injectors.