This is a conundrum. You want a 1K hunting rifle where even only on rare occasions you will hunt elk. IMHO, unless you go with a really hot 7mm, it just isnt in the cards. Sure any old 7mm can kill an elk at 1K but the goal here is to have it done a cleanly as possible. You need enough velocity for bullet expasion. For the average 7mm, this is a bit much to ask at 1K. At least with a bullet suitable for elk. The AMAX would expand at that range, but put it in the wrong spot (IE shoulder) and you will most likely be hating life.
I understand your position on recoil and barrel life. I too make these a priority when concidering a new build. A 7RUM and STW is a bit more than you want but the 7mm Rem, 7mmWSM or SARUM are all great choices but fall short of being a legitimate 1K elk rig. So, you will have to shorten up your max range on elk or go bigger.
That said, I have been interested in a 7mm for a while. At some point I will most likely build one. I have narrowed it down to the 7mmSARUM OR 280AI for an assortment of reasons. 1: They are very efficient. 2: Have nearly the same potential as the 7mmRem with less recoil and powder as well as better bbl life. 3: The 280AI has great brass options available. You can get 30-06 Lapua brass and neck it down to 7mm. There is no Lapua brass available for the SARUM but I feel this will change. Lapua gets ALOT of requests for it as more match shooters are starting to use the 7mmSARUM. Much more so than the WSM or Rem mag. In any event, the 280AI will be built on a LA and the SARUM would be best on the LA as well. So it is a tough choice for me. Both have a reputation for being very very accurate. With the 162 AMAX, you have a very legitimate deer and antelope rifle. The 160 AB or IB is great for elk, but should draw the line between 650-700 yards. If you are one that throws the 1500'# rule out for elk and just go with expansion, you could stretch it to 800-850 depending on your velocity etc...Thats at elk altitude.
Everything is a trade off. If you want a 1K elk rifle, do it right. If you can live with a reduced range for elk, any of the medium 7 mags will do what you want for deer and antelope.
To run your 180 VLD at 3000+ in a 7rem mag or WSM etc...will be high pressure loads. Barrel life will be as short or worse than a bigger 7mm. If you want higher velocities than what the Rem mag or short mags were made for, go with a larger case and save your action and brass.