3:73 and 4.10 gears & mileage & Anyone have towing issues for 2009?

We have had transmission issues towing a camper. Just installed 2nd tranny in one year. Just got a new reman GM trans. Considering keeping the avy and changing out the 3.42 gears. If 3.9 was available for the front IFS I'd be all over it, but looks like my choice would be 3.73 0r 4.10. I'm concerned about mileage though as it is a daily driver.
Can I get some mileage reports on anyone's 2009 or 2010 4 X 4 avy with 5.3 / 6 speed
*** IF YOU HAVE > 3.73 & /or 4.10 gears?***
Towing feedback would be greatly appreciated too. I'm baffled why this thing doesn't want to tow our camper pushing or just over 6K loaded & with us. Struggles on hills and well the track record is the transmission breaks every 2nd or 3rd trip.
we are considering just finding a clean good running 2003 - 2005 2500 avy as strictly a tow vehicle. gears would be cheaper though.

I have a Cold air intake- cat back and diablo sport tune with tow tune installed.

I say 3.73 would be your best option. Although not optimal for daily driving, if you are towing on a somewhat regular basis, I have found the stock gears suck. I have the towing package on my 2009 but have the 3.08 gears. So I feel your pain. Plus my custom steel bumpers, 7.5" lift, roof rack with full spare, 35" mud tires, etc etc it sucks some fuel. In your case, the 3.73 would be as low as I would go simply because, 3.73 on all of those specific transmission ratios is pretty dang low. 4.10 just seems way overkill to me. I am no guru by any means, but that is what I think you should do. Also, do you have a trans cooler? Heat is deadly for transmissions. So you may want to look into one of those if you dont already have one. For me personally, I am going up to 37s and swapping to 4.56 gears at the same time. Should drive a LOT better with the low gears. Although according to the gear calculators I have used 4.10s would be optimal, my truck and setup as far as aerodynamics and weight is FAR from optimal so I would rather have a little extra to keep it moving forward. Hope this helps you out man

Yes, installed trans cooler after 1st one over heated and then started slipping really bad. Actually wouldn't move at one point. For some extremely stupid reason starting around 2008 Chevy made a trans cooler an option. Even when equipped with the tow package.
The second one just instantly broke. May have been a bad component in the reman, but still concerned about the 6 speed.

I havent had an issue with mine yet, knock on wood. Had a slight whine and noise to it. Changed the fluid, never made another peep. Heard clunking recently and it was just the U joints and the common GM slip yoke thing. Replaced the U joints and greased the slip yoke. Not its quiet again. Trans cooler helps a lot with towing, or mine does anyways. So it should be even better when I have to tow with the lower gears.

6k is a lot of weight for any 1500 Av. I have 3.73 gears and still would prefer 4.10s, even with my supercharger. My boat is 6500lbs and I run 3rd gear exclusively unless the terrain is perfectly flat.

How many RPM a you running when you're at towing speed? Final gear ratio is of more importance IMHO.

EDIT:
Just saw you are running a 6 speed. This is apples and oranges. I don't think you need more gear. You may need a HD tranny.

If looking for an HD tranny 6L80e I would suggest the transmission center. Monster has a slightly upgraded one but its not as good as one of the ones from the transmission center. Theirs can be built to handle up to 1200 hp

Thanks for the responses. I really wish I had looked into it when the 1st one failed or wish the shop had offered an HD transmission as an option.
We switched gears though- "in thought process". Were going to get an older 2500 avy and use it for carting around town on occasion and towing. Keeping the 09 and leaving gears as is. Would have liked 3:73's in there though. Woulda pepped it up a little.

I say just upgrade your current truck to be able to handle the load. One less note. Less insurance. Less gas. Etc Etc.