'04 Tahoe 5.3L 3.45s RWD. My guess is a lack of torque around the 2000 rpm range. So what can we do? It is really annoying. Sometimes it will even slam down into 2nd.
Not doing 3.73s.
So do we go to a 6-6.2L with a small cam? Smaller than stock cam for power below 2000 rpms?

 

Stock 6.0 alone will make a huge improvement and is recommended.

 

You can change it in the tune- I have the same issue with my 02 on 285's so I changed it.

It does however now loose speed going up hills but it doesn't downshift.

When it's has cruise control on it has stock programming and does what factory intended it to do

 

You need a supercharger and a tune to match. The supercharger will keep you moving, the tune will keep the transmission in gear. More torque means you blow up the transmission on the second hill, but hey, it held for the first one didn't it?

If you're wanting to hold gears, in a heavy *** SUV, you need to get a 4L80E (which is designed for that...stock). You'll almost immediately burn up the 3-4 clutches in a 60E if you force hold them under load.

 

Why exactly are you against the gear change? I swapped from 3.42s with 275/55-20 and went to 3.90s my highway mileage improved about 1mpg and my city mpg improved 2mpg. Not to mention it feels so much lighter at all times. Yes a tune would help as well. If you tow at all it will be a huge improvement.