The 5.7 liter Tahoe is a great vehicle, but nothing you do and no amount of money dumped into will make it a suitable tow vehicle for a 31' Airstream. I have cut and pasted my response to a similiar question on an earlier thread. I suggest you look for a used Suburban or Yukon XL with either a 6.0 liter with 4.10 rearend or 8.1 liter with a 3.73. Read on for more details. Bear in mind, I'm discussing personal experience with full size Suburbans. A Tahoe is inherently unsuitable and unsafe because of its short wheelbase.
From 1996 until May 2005, I kept looking for marginal, incremental improvements in towing while balancing fuel consumption not towing.
1996: 1995 2-WD Surburban with pre-Vortec 5.7 liter (350 cu in), 3.73 rear end, pulling 1976 Airstream Safari 23'.
This wasn't a bad combination in coastal Carolina and the east coast where we lived at the time, but it didn't do well in the mountains of NM. (11 mpg towing and 17-18 mpg combined).
2001: 1999 4-WD Surburban with Vortec 5.7 liter, 3.73 rear end pulling 2000 Airstream Safari 27'.
The added power of the Vortec engine was offset by increased weight of 4-WD and larger trailer. Performance in mountains was marginal. Non-towing average MPG was lower than 1995 Suburban. (11 mpg towing and 15-17 combined)
2004: 2003 4-WD Z71 Suburban with Vortec 5.3 liter, 3.73 rear end pulling 2000 Airstream Safari 27'.
The advertised increase in horsepower of the 5.3 over the 5.7 is great for non-towing, interstate highway cruising; but a big disappointment for towing. The extra horsepower comes at higher RPMs and results in less torque and marginal towing performance on mountain grades.(12-14 mpg towing and 17 combined)
2005: 2005 4-WD Silverado 2500 HD with Durmax Diesel pulling a 1976 Sovereign
31’. A towing machine, but not a very good vehicle for driving around town, so I bought a 2005 Pacifica for city driving.
What do you need? I need 4-WD, but if you don't otherwise need 4-WD, stick with 2-WD. That gives you 500 pounds of additional towing capacity and improves your non-towing gas consumption by about 2MPG.
If you want a tow vehicle that must double as your non-towing, take the kids to soccer practice, family car; the 1500
Suburban 5.3 liter is a nice compromise vehicle if you can find one with a 4.10 rear end. If you want to optimize mountain towing, look for a 6.0 liter with 4.10 rear end. If you want a towing machine, and you care naught about MPG, get the 8.1 liter and the 3.73 rear end.
Bottom line... you will never be satisfied with 5.3 liter and the 3.73 in the mountains, but it's the most fuel efficient combo Chevy offers (12-14 mpg towing and 17-18 mpg combined maybe better with 2-WD and keeping your speed below 62 mph.
The 4.10 rear end behind the 5.3 will make you less unhappy, in the mountains and may be all you need. The 6.0 liter with a 4.10 will make your heart sing in the mountains, but make your heart will ache at the gas pump (11 mpg towing and 13-14 mpg combined).
Another option is to buy a beater car to drive around town, and buy a dedicated towing machine for your road trips.
Hope this helps.