Check the case length after you run the 7-08 through you 308 die. I accidentally ran a 7-08 case through my 308 die and the case came out a bit longer than my 308 brass.

As you have already found, it's not a problem (although 7-08 brass is most likely more expensive than .308, so you could probably "ebay" your 7-08 brass and buy twice as much .308 brass with the money).

Necking "up" as opposed to necking "down" tends to give you a little less uniform neck thickness, but going only from .284 to .308 shouldn't create much of an issue.

Just run it through the sizer (but only deep enough to chamber readily in your .308), load, and shoot. No need to "throttle" back on your loads, just shoot whatever normal .308 load you use.

You won't wear out your die. You should be able to load and go.