Besides the 6.5 prc

One issue with the 270 (depending on budget) is most factory rifles aren't going to have the twist rate for those new longer bullets. Lots of options to get you there, all depends on what you're willing to spend, what you want, and what your "all day" recoil tolerance is.
I was going to build a rifle, well I won't I'll have area 419 build it... Just curious if a 270 with these new longer bullets could do it... My buddy has made 1 st round hits with a 6.5 x47 out to 1500 yards and hit at 1600... It's just for fun, not that I wouldn't mind trying a competition...
 
I'm using a 7rem mag 1:8twist with a 28" barrel. My load with 180hybrids is 3052fps and stays supersonic to 1790yds give or take at my elevation of 2500.
I use 195tmks in my 308 and have used them accurately out to 1500 and they transition around 1200 so shooting into subsonic is very doable and a lot of fun. Depends what you're looking for I suppose.
 
338 edge, 340 weatherby, lapua, 408 cheytac. All of these in a light rifle are painful, but if you are building/wanting an all day range bench rifle, you could have any with some heft and good barrel and have at it. Get out your checkbook. Order of expense 340, Edge, Lapua/Cheytac. Now that I think about it, I have never heard anyone on here mention the Cheytacs? There must be a reason, but no idea what it might be.
 
That 6.5PRC with the 156g Bergers can be pushed to about 2800 fps without too many issues out of a properly built rifle. They should stay supersonic out to 1600 yards and just barely supersonic out to 1700 yards and should just be falling under the supersonic threshold at your mile mark. You can push them faster, but work up gradually and look for signs of pressure build up. I have heard that getting close to 2900 fps and you start seeing some pretty significant pressure. They may go the mile accurately in your rifle. They may not. The only way that you will know for sure is to try it out and see.
 
**** near every cartridge will get you to 1mile. Watch "mark and Sam after work" on YouTube. Aussie folks that do a pile of shooting. They got a .243 to 1mile. It's doable. Just a matter of how much time you want to spend developing loads. Bigger, faster, higher BC, will be easier to do it with. Get multiple decent ballistic apps and start running different bullets and velocities and see which ones will get you there with the equipment you have available. Sure a 3-9x Bushell $100 optics can see a 1mile target but if you don't have the elevation and consistency in it you might as well just grab the bullets by hand and toss them in the air.
 
I have three rifles that will do it or very close to it . First a 270 Win with a 1-8 twist heavy barrel loaded with 170 gr EOL Berger. Next a custom long throat 284 Win 28" 1-8 twist heavy barrel with break. Either 185 RDF's . 195 EOL and 197 SMK's. Last a 338 Win mag 26" 1-10 twist either a 250 Berger at 2,850 or a 300 Berger at 2,500 will just get you there as well Supersonic.
 
Besides the PRC... are you looking at a short action or long.....6.5x284 is excellent. 280AI. Lots of good choices actually. Each caliber seems to have a decent line up of quality bullets and components to get a shooter to a mile with the right barrel twist etc. I have 22" proof 6.5 PRC that is running 156's at 2900. I am running 135's at 3090. So everything in between is around 3000.
 
Seems any cartridge caliber between .338 and .243 has been mentioned... it's subjective as to what you consider is something you "can shoot all day".... good brake will help. 6.5 and .270 calibers are very capable .... for a short action application to be used with heavy bullets that will not only reach a mile but do so consistently and accurately the 6.5 Sherman Short, .270 Sherman Short and 7 Sherman Short will meet your criteria. I researched and after having some success with the 6.5 PRC decided I wanted a cartridge designed to chamber a wider variety of heavy for caliber high BC bullets in a short action magazine length COAL. The 7 Sherman Short was my choice and I have 3 barrels chambered in it. I am considering a 6.5 SS for the 150 class bullets and a little less recoil. That said the 7 SS with 175-197 grain bullets and the sidewinder brake is pleasant to shoot. So many options for you as mentioned, and this is from my experience for what it's worth.
 
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