I feel bad for the OP...five different places have given her (?) five different causes.
If mech #5 is right (that the ATF and coolant have cross-contaminated each other due to the two compartments in the radiator being compromised), that is pretty bad. It *could* be the reason why the ATF was 'thick as paint' and 'black' (but that is just a guess, from the info we have).
If they've intermingled enough, what's in the coolant reservoir (white plastic tank with a black cap on the top with 'DexCool only' printed on top) will look similar to a strawberry milkshake. If you see that - the two have definitely intermingled (the auto trans fluid is routed through a separate compartment at the bottom of the radiator to provide cooling for the ATF.) If you don't see it in the reservoir, you may be able to detect it in the radiator, but it will be harder to detect there, unless you get something to extract a sample of the fluid (e.g.; turkey baster, etc.), and transfer it to a container where you can view it & examine the consistency (which should be similar to water, if all is well...and the color will be orange, as well). Note: Do NOT open the radiator cap after running the engine / driving the vehicle. You want to check this when the engine is 'overnight cold', so that you don't burn yourself.
Besides the radiator replacement, the cooling system will need to be completely flushed, and new DexCool (GM's name for their brand of antifreeze) installed. As long as the source of the leak is repaired, the engine should be OK afterward.
Now for the really bad news (again, if the coolant got into the transmission)...
Coolant / water inside of a transmission will damage it in short order (by swelling the seals & clutch material). There are two ways to 'fix' it.
The first is to replace all of the fluid in the transmission & the filter - and hope for the best. Unfortunately, some coolant tends to stay behind, especially in the torque converter, and that 're-contaminates' the transmission again (in truth, it was never properly 'de-contaminated). It's a roll of the dice as to if / when you'll start having issues with the trans (which may be as 'little' as fluid leaks developing, due to swelling of the seals - but the transmission otherwise continuing to operate 'fairly normally'... OR...an actual failure of the transmission, due to internal parts being compromised).
The 'correct' way to fix it (per GM)...is to remove & rebuild (or replace) the trans. At a minimum, you need to replace the following:
All of the rubber type seals
All of the composition-faced clutch plate assemblies including the band.
All of the nylon parts.
The torque converter.
Then thoroughly clean and rebuild the transmission, using new gaskets and oil filter.
Obviously, that looks like a lot of $ - and you'd be right to think that. It's probably cheaper to replace the transmission (either with a used one, like from a junkyard, or with a new / rebuilt one).
Now...with all of that said...and again, *if* the contamination issue is 'true'...
- You've stated the trans seems to work 'normally', currently (except for the codes, of course)
- You don't know *how long* the coolant has been in the trans (or how much), since you just got the vehicle.
- Given the above, it it were 'me'... I'd take the cheaper solution first (let's call it 'flush & pray'.) It may work for a day, a month, a year - or for as long as you have the truck. It will definitely be cheaper / less downtime than rebuilding or replacing the trans now.
Also, and I'll add this, based on the info you've provided us so far...
- "prior owner didn't maintain the vehicle"... in order to be more sure on this, you'd want to (have someone) inspect the entire vehicle, to gather evidence of same.
- Radiator failing at your mileage... it can happen, and the most likely cause would be if the original coolant had been left in it waaayyyy too long (or an accident of some type in the past compromising it, but then you'd likely *see* a leak)
The factory fill is rated to last the longer of: 100,000 miles *or* 5 years from new. What happens is that the coolant loses it's protective qualities and turns acidic - and you can figure out the rest. I can't see as I write this response how 'old' your truck is...but I seem to remember it wasn't too far over 100K miles.
Right now, except for the price you paid for the truck, you don't have a lot invested into it (time, parts, etc.) Depending on how much you paid for it, you may decide to just sell it for what you can get (if you sell it privately, it's best to tell the potential buyer what you know about the condition of the truck).
Finally, to answer one of your questions directly...
>>>1. Could this have really been what was throwing all of those codes the whole time?
Possible, especially if the trans has significant coolant contamination, and it has been going on for awhile. However, if that turns out to be the case, I think you'd be having more / other issues than that.
(I've kinda addressed question #s 2 and 3 above, so no need to rehash those)
The next step for you is to figure out which mechanic(s) are steering you correctly, and go with the one you trust (or can show the most positive feedback from other customers...and that's not #1, in our opinion).
Sorry to be the bearer of bad news. I wish it could be better.