Mag, I've only had two of the three you're asking about, the M700 SS Mtn, and currently the M70 EW.
The Rem 700 SS Mtn Rifle happened to be a 280. It was the first Gen from the early 90's, an ADL w/ tupperware stock. As was noted, it has a fairly slender bbl. contour (unless the one you reference has changed).
The EW is an outstanding rifle (mine is ridiculously accurate) with enough "heft" to settle down. Were I in your shoes and wanted a LA, that's what I'd pick in 270 or 30-06 (though mine is a 308 and that's what I'd chose - or 7-08). I much prefer the 3-pos safety that locks the bolt over the 700 safety that doesn't - climbing around in the mountains I've had 700 bolts open too many times to count. Also, the 700 safety slot is a pathway for water and snow into the trigger housing. Have seen the trigger ice-up to uselessness in the right (or wrong) conditions.
Like others, I swapped out the M70 B&C factory stock for a McMillan Compact Edge, and added PT&G aluminum bottom metal. It is still light enough to pack, but heavy enough to settle down. I'd prefer it in a deer stand over the Remington every time. Ditto on the mountain. Like was mentioned, run the factory stock and see what you think. You can always sell the stock and get a McMillan later.
The Sako... well it's incredibly ugly. The magazine makes me throw up in my mouth a little...
My 308 EW, 7lbs 12.5oz's scoped, with sling and 4 rounds... at home in the mountains or on the flats: