I run El Paso to S. Florida regularly. Across Texas much of it has an 80mph speed limit which of course you won't try to match, right?
Cooling and A/C are primary. As suggested, flush and change the coolant and clean the condenser and radiator thoroughly, and the evaporator to the extent you can get at it.
Is it an electric or mechanical radiator fan? I might change the motor or clutch for new before the trip, if they're ~100k miles old.
I'm also a big fan of Chevron Delo ESI 85-140 if you haven't renewed your axle lube.
Yea I just did the trip last month without a trailer and running 80mph got things a little hotter than I like. Engine core temps got up to 245.
If I tow a trailer I will certainly limit my speed to 65 to 70.
I have an Elect fan cleaning out the cond. and rad are probably a good idea my evap has a filter and probably about due for a change. I think the coolant is two years old and I also have water wetter in it. I should change the trans fluid and rear lube too.
Heat is no big deal... It's much cooler in Louisiana compared to our 115 plus summers here... And you dry heat guys... lol The fact is if it hits a hundred plus HOT is HOT... and 95 with humidity is easy... Plus I grew up in So. Florida and humidity is easy...
Short answer: go looking for the problem(s) that you think might sideline your Tahoe before your trip.
Longer answer: you should have a reasonable idea of what you haven't spent any money on repairing / replacing in the past few years.
Ignore anything that is neither important nor urgent, until you determine the relative state of the important / urgent stuff.
If it's been more than 3 years since you refreshed the coolant, why not? Check coolant connectors.
Buy spare relays & fuses, plus extra antifreeze ... & H2O for y'all.
How long has it been since you serviced the AC? Would you consider installing one or two helper fans on your ATF cooler or radiator?
I'd be surprised if you don't know at least one mechanic who can help you apply pragmatic pessimism to answer your question more specifically.
Since I do a lot of running in the wilderness I carry a lot of spare parts now but, some relays might be in order.. Thanks for mentioning relays.
In my past life I was a auto tech but, It never hurts to query with some of the experts on here...