Towing in 3rd gear on a 1300 mile trip

I have the 5.3 bolted to a 4L60e on a 17 year old Suburban. My engine only has 40,000. Don't know the history of the transmission but it's tight. I let it engage OD if it's not jumping back into 3rd a lot. If it is I pull it down into 3rd. I keep my speeds reasonable and let it rev. I find that if I don't get in a rush and let it drop off a little speed when it needs too it doesn't hunt that much, till I get into hilly country. I just leave the tow/haul on and let it do as it pleases till the hunting starts. My buddy had the 1500 truck with the 5.7 and 4L60e and he put over 300,000 on that thing pulling trailers full of furniture in the mountains very frequently. I suspect he had the transmission worked on, how could he not? He claimed that it was all original but, I'm suspicious. His son totaled the truck last year so, it's a mute point now. Anyway, great vehicles. Just be reasonable with it.