Thinking out loud here...
1) To get lower recoil, generally you'll want to go towards lighter bullets, and slower velocities.
2) To get to 1k reliably you'll need to have the bullet still traveling mach 1.2 at 1k yards.
3) To get more barrel life you want larger bore diameter, less powder, lower pressure, a longer case neck and cooler burning powder.
So to accomplish both #1 and #2 together you would want to use heavy for caliber bullets, in a smaller caliber, going slow as possible, with a longer barrel. You'd be after something with the best BC/weight ratio. That would have me looking at the 6mm 110 SMK or the 22 cal 90-95gr bullets. Unfortunately I think once you step down to 22 cal you lose too much on barrel life. For example A 22 Dasher is going to have less barrel life than a 6 Dasher, simply on the principal of similar amount of powder at similar pressures being forced through a smaller diameter bore. So if you pick the 110SMK, you need to be able to get it going about 2650fps to make it to 1k yards.
Moving on to #3, I poked around in Quickload looking at the cooler burning powders like H1000 and some of the Vihtavuori slower burning powders. H1000 is a bit slow and bulky to make the necessary velocity until you get up to a pretty large case. N165 is even cooler burning, but again too bulky. The best choice I could find was N160, which is about the same burn temp as H1000. It needs a case that's bigger than the 6BR but smaller than the 6x47 to hit around 2650 fps at between 45-50k PSI. Something like the 6BRA or Dasher gets you closest, with the BRA probably being better due to smaller capacity and longer neck.
If you picked a 6BRA or Dasher 110SMK N160 combo you'd be at around 33-35gr pretty compressed load 48k PSI at 2650 fps from a 26-28" barrel. I plugged that data into the "barrel life calculator" spreadsheet that someone made a while back (based on pressure, temp, amount of powder) and it predicted a barrel life of ~4200 rounds. Not quite your goal of 5k barrel life but getting close.
Only problem is that you're looking at needing to buy hydro brass (can't fireform if you want to avoid barrel wear) plus custom dies and a semi-wildcat cartrige. And there'd be no guarantee that it would be accurate or make the necessary speed or not give you issues due to loading compressed powder charges. And N160 can be harder to find and is more expensive.
IMO what I would do instead is build a straight 6BR and shoot 105's at a conservative 2800 fps from a 26-27" barrel using Varget. It will get you probably around 3k barrel life, be relatively low recoil, and is a well established easy to load for cartridge that is a proven accurate performer.
