Sorry I didn't read your post carefully. OK if I had a .270 already I would definitely NOT get an 06 as they are too similar in my opinion epecially on deer size game. Not sure what type of cover you hunt but the .270 would certainly handle the long shots. If you hunt closer cover I would take a look at a bigger bore. I and many of my buddies use .358 wins (now available in a BLR again), .35 whelens and .350 rem mags. As already mentioned the .45-70 and .444 are also awsome deer killers.
A good 3 gun deer battery would be:
.270 bolt action
.358 BLR Lever or 45-70 Guide gun
.300 magnum.
You would be covered for everything in north america.