Yeah it definitely doesn't run rough on start up at just has the ticking/tapping sound for 45 seconds. Have you or anyone ever tried adding Lucas Heavy Duty Oil Stabilizer or anything similar to the oil to try to eliminate the ticking/tapping sound? Is it possible that the coolant could be causing this sound on startup somehow?
I have a 01' Denali 6.0...
Every morning, when I start her up she too plays the taps...I got her in 04' with 40k and as the years went by, she now has a 126k, the tap got louder... Just by listening, I traced it to the front of the driver side...
( Coolant has a way of disappearing on mine too, I just keep filling her, I all ready know it's my water pump... check the water pump first from the bottom of the car, also the sides of the radiator ;like the dude said earlier, if coolant is passing thru a head gasket you'll see and smell it in the exhaust... also on the rough Idle, theres a bad flaw in the oil separation design, on the 6.0 it gets routed right behind the throttle body and leaves a thick residue film all over the interior walls of the manifold, I shot two cans of brake cleaner and throttle body cleaner right up the body while I was parked on a a incline, let me tell you what... it ran back out like the blackest of black you've ever seen, now, no more rough idle... remove the air flow housing to the throttle body and lift the butterfly, look behind it and/or stick a finger behind it a wipe it around in there if it comes out anything but clean shoot some cleaner up there and stick a rag as far in as you can get to wipe it clean as best you can.. )
I consulted a few mechanics and most agreed that it is a lifter that sticks a bit until the oil pressure builds enough to lube it properly...
Hence why it goes away quite rapidly and why it only happens after sitting for long periods of time...
I tried the lucas after I made a huge mistake, at work and decided to do a quick oil change, had my Mobil1 filter and Synth Oil, Drained it, removed old filter and installed new one... The Bad - I didnt notice that the old seal did not come off with the filter

...
So i'm all done, go to start and within 5 seconds all my fresh Mobil1 was on the floor and no longer occupying the space where it belonged

...
So hear I am miles away from any auto parts store, so what do i do? ...
I Drive concrete trucks, so I go over to the shop, siffon off 5 quarts of heavy weight truck, oil filler up and go on my way

with the intention of just making it home 12 miles away and changing out for the right stuff the next day...
Low and behold I wound up driving it with the heavy oil for five days... now it the morning the tapping is still there and a bit more prominent but still goes away with in 45 seconds...
I added Marvel Mystery oil and Lucas and both helped a great deal..
Even though its most common knowledge that when you get an oil change rule of thumb is five quarts... not so in my case.. the 6.0 needs 6 quarts..
This is why this sound occurs in most engines... ( in my opinion )
I don't care what mechanic, dealer, book tells you to do.. add a half to a full quart extra dependent on what size engine you have... ( once more, just my opinion )
The book the Denali came with actually says fill with 6 quarts...
After years of just using quick lube joints that don't know any better and fill with five quarts instead of six hear we are...
Try the Mystery Oil first... or the Tranny fluid sounds like a great idea... i'm going to do that tomorrow ... and I think I'll go back to the real oil too, you cant believe a word " THEY " say, for all we know synth oil could very well be crap.. Trust no one...
Sorry if i went over-board with my reply.. it's late, I'm Drunk

... Good luck.