Here We Go Again! I need to build a Mule Deer Rifle

Fast twist (1-8) 6.8 Western will easily cover your needs. Reload the 150gr Badlands SBD II and you can get your practice in busting rocks way out past 1,000 yards in preparation for hunting season. That bullet has a 0.35 g7 BC!
But your 6mm Creedmoor is probably more than enough and Badlands makes a sweet little 100gr bullet that would work very well in the Creed.
 
6.5PRC would do you well on mule deer. It will work very efficiently out to 400yds and well beyond. Took this muley doe with 143eldx bullets at 3025fps at the muzzle. DRT.
 

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I built a 6.5PRC with a 20inch carbon barrel for fun. I could not be more pleased with accuracy and hunting results so far only out to 500 yards. But in reality, a 308 win is all you need.
 
Stay with the .270 Winchester. Ammo, brass, projectiles are readily available and is the perfect 400 yard mulie caliber. Not new or sexy, just perfect!
The .270 I have is a 1957 J C Higgins (FN action) action that I was given in 1968, has a newer Hart barrel. The scope mount base screw holes are not true and can't get but two out of four screws in it. Never been able to get much better than 2" groups consistently, which doesn't provide much confidence for longer shots. I love the old gun and retired it some years ago for that reason. I took it last year due to peer pressure that 6mm was too small.
 
A wise fellow once told me "bullets matter more than headstamp".
Maybe figure out what bullet you're going to use and then build or buy a rifle around that bullet at your desired velocity.

The Hornady factory 108 ELDM ammo and the Berger factory 105 hybrid ammo sure works well in my 6 creed.
I shot one last year as stated in OP with 103 ELD-X
 
Based on your criteria I say go 7-08. There's definitely factory ammo around, but you can hand load it and really make it shine. I was looking at Hodgdon load data for the 7-08 and it looks like with Staball 6.5 you can push the 162 Hornady eld x and m to 2800 in a 24 in barrel. Shooting it at 2700 fps at my elevation of 4500 ft gives you 1800 fps at 800 with 1200 ftlbs of energy with the m. The x is at 1793 fps and 1150 ftlbs. So both are stellar for deer to much farther than your stated distances. I wouldn't hesitate to use a 162 eld m on a deer. Took my elk this year with the 162 eld m from my 7 Mag and it was traveling roughly 2700 on impact. Did it a fantastic job. 7-08 gets my nod for low recoil potent round. Plus in my mind its not as common as others so it gets cool factor.
 
I gotta know… what happened to the 270? And what rifle were they gonna let you "borrow?" And were you in the US?

(Feels like that episode where Jim Shockey goes to hunt in Mexico… even he had to slink out of there.)
Slipped on iced up running board getting out of Jacked up truck, landed on top of gun, bolt open, magazine in hand, in the rocks, barrel full of snow, two broken ribs.
I was the only person there that wasn't shooting something that ended in Magnum. I had brought the 6 Creed on the off chance a varmint hunt was possible.
 
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