Three great calibers and I would not hesitate to recommend any of the three.
If you still have the .270, then I would opt for the 7-08 or the .308 in a short action, handy rifle such as the model 7 or the tikka lite or the browning micro medallion. You can get by with an 18-20 inch barrel in the short actions, but probably would want 22-24 inches in the 270. By doing this, you have two guns that you can use for different applications (i.e. stand hunting and deep woods/stalking). All are at least 300 yard whitetail rifles.
Of the two, I really love the 7-08 because I have a fondness for the 7mm class of bullets. Currently, I hand load for 7mm Rem BR, 7mm-08, 7mm-08 Ackley Imp., 7 x 57, .280 Rem, and 7mm Rem Mag. I usually don't have much trouble making a 7mm shoot well in a short amount of time.
I don't think you would se any major recoil difference between the 7-08 and the .308, but if there is, the 7-08 should be less. Also, it is popular enough that just about any gun store, sporting goods store, or wally world should have a good selection of loaded ammunition for it.
Hope all of this helps,
Smoky