A 270 Win with the right loads would be great elk medicine. I would look at a heavier slug from Barnes. As for changing calibers, they should use the same bolt head. Only issue would be with the magazine as a 270 is on a standard or long action, and the 308 Win is a short action. Won't matter for the bolt throw, but the magazine would probably have to be changed out and that CAN be a bear on a Savage, depending on specific magazine used.
Converting it would probably run $3-400. You just need the wrench, a new recoil lug, barrel, and headspace gauges. Personally, I would go with the 270 Win and never look back. Use the correct bullet and put it where it belongs, and you will have a freezer full of elk steaks. JMHO of course.