A 5.3 would be fine for commuting, but you would be pushing it pretty hard for that kind of towing.
For reference, a 5.3 or 6.0 from a suburban/1500 will have a 4L60e/4L65e behind it. Going up to a 2500 donor would get you the 6.0 and a 4L80e that will stand up to towing loads much better. A 6.0 with lean cruise enabled will get comparable mileage to a 5.3 for commuting while keeping the higher power available for towing.
As far as whether the 5.3 would do the job if you kept it slow, I would say that depends on your gearing, tire size, and definition of slow.
The 2007+ have the AFM/DOD system that is prone to rampant failure. If you are planning to open it up begore the swap, you could remove that system and put a standard cam/lifter set in it. If you want to just make the swap and be done, I would avoid that version.
The 07+ engines also use a new/different ECU that is much more prone to failure than the 00-06 version. It can be converted or you could put an aftermarket engine control on it, but this sounds like a project that you want to do faster/simpler/cheaper than that.
As a point of comparision, I put a 4.8 from a 2000 1500 in an 84 half-ton truck with a 3.55 rear end and 27.5" tall tires. I rebuilt the 4L60e with upgraded clutches and an 1800rpm stall converter. Commuting to work at 70mph, I get between 19.2 and 20.1mpg consistently. Going cross-country at 85mph, I get ~17mpg. If I pull more than about 2500lbs, the torque converter basically never locks up. Above about 4000lbs and it won't hold overdrive on the highway.
That said, older trucks didn't *have* overdrive, so that isn't bad compared to them. But my Yukon with the 6.0 4L65e will hold lockup up to about 4000lbs and use all of the gears up to its rated 6500lb towing capacity. In trade, it gets ~17mpg both commuting and going cross-country at higher speeds.
For my specific purposes, I am happy with the decision to put the 4.8 in because it was dirt cheap, dead reliable, and gets better mileage in all use cases than the original engine did. For 98% of the time, I am towing less than 3000lbs with it and the slightly higher mileage is worth it.
Another thing to consider is that I have it set up fully legal with both cats, egr, evap, etc for an 84. If you are putting it in a truck from the 50s, that extra equipment is not required and you can squeeze some more lean cruise out and have more tuning flexibility.
