If that 110E is a 30-06 now, then it should just be a 110 Long Action with a Staggerfeed magazine (5.062" between screws). Only way to know for sure is to measure the distance between the action screws. Here is a link to the measurements.
If that is what you have then here is the follower:
Using the follower you should have a trouble free transition to 308 from a 30-06. Try the magazine also, I have had great luck getting the 308 to feed from a 30-06 magazine if you want a repeater.