Update.
I replaced both 'T's with new GM 'T's, and it was still a royal PIA. I purchased 2 'quick disconnect' tools, but neither on worked, so I might as well have flushed the money down the toilet and saved the commute time to the parts store. I had to cut all of the quick disconnects with a hacksaw blade to remove them in the method that I previously described. To accomplish this task, I had to stand on a step stool, bend over the passenger side front fender, lean down over the motor, and then twist my upper body to the left, to get my arms in a position to access the 'T's. This was real interesting, to say the least, as I had my left shoulder replaced 8 months ago, and it is still healing.
Needless to say, as an old man, I am sore from finger tips to toes today. I even cut my fingers in 2 places, as a result of having to use the bare hacksaw blade. But, a PIA job needs to have the subsequent aches, cuts, and bruises, in order to justify it being a PIA job.
One thing to note for folks performing this task in the future. Wear gloves, as the sound deadening material wrapping the underside of the cowl, over the 'T's has a fiberglass material, similar to old home insulation that gets into your skin, and the back of my hands still itch from the contact with the material.
I've also replaced both radiator hoses and the coolant bypass hose, all of which were original parts on the truck with 2007 date codes. I used new screw clamps, replacing the original spring clamps. I am now waiting delivery of both heater hoses, scheduled for tomorrow.