There really isn't a good reason to size down 308 brass if the properly marked 7-08 brass is available.
Mind you, with the price of a bag of brass cases these days, maybe there is a good reason, especially if you can get some once fired cases or even range brass to neck down.
I've modified cases to fit on several different cartridges when the proper ones just aren't available or often, a couple of bucks apiece.
I have swaged down the 308 case to 257 and expanded the necks to 338 and 358.
When I reduced the case neck to 257, I annealed the the neck and shoulders on once fired brass to dead soft. To soft for good bullet retention IMHO. The 25-08 is a fantastic performer by the way. Even though the case capacity is within a few grains of the 257 Roberts, in modern rifles it can be loaded to some very quick velocities, even rivaling the 25-06 with all but the heaviest bullets.
The 7-08 is a shooters dream. Because of the modern rifles chambered for it, and because of case shape it is the kissing cousin of the tried and true 7x57 but able to load even heavy bullets into the case without taking up powder space, even in a short action. The loads given in most manuals push similar weight bullets faster than the 7x57 loads which of course are held to lower pressures because of the older and supposedly weaker actions it was designed for.
Time to get back on topic. I went to the loading bench with a couple of once fired 308 Win cases from the appropriate bin. The cases, were Winchester, not my favorite but if these worked, anything will work.
I cleaned up the brass and lubed the inside of the neck as well as the outside of the case. Then, I screwed in the full length sizing die for the 7-08, put in a #2 shell head holder and inserted the first case. It went without a hitch. Of course, there was a bit more resistance than usual but not enough for the RCBS JR press to notice. There would be even less in a Rock Chucker or something similar.
I never noticed any thickening of the case neck but I did notice that it was to long and the case mouth wasn't even. It was uniform in thickness all the way around though. Yes, differing thicknesses around the neck can cause some minor accuracy issues. Only if you're really anal though or a bench rest competitor, which is basically the same thing. The extra brass has to go somewhere, if not into the sidewall of the neck, then it has to go onto the end around the case mouth.
The second, third, fourth and fifth cases all swaged down smoothly as well, with only one pass needed to get it all the way down to the base of the neck/shoulder. All needed to be trimmed for length before loading.
The reason I was curious as to how easy this would be is because with the 25-08, if I didn't anneal the necks dead soft, the shoulders would collapse on many of the cases. The next batch of cases were made by necking up 243 cases and fire forming with the first load. There was no indication of this happening at all on necking down to 7mm. You might want to set the shoulder back a bit as well. Some chambers are a few thousandths of an inch shorter and your case body/shoulder may be a bit long. I loaded these cases with 160 grain bullets over W760 and CCI 250 primers. At least they will be useful. In my box, these have RED colored bases, done with a RED Sharpie. I have put a note on the underside of the lid to explain what and why the RED bases are about.
You may want to do something similar. I really have an aversion against cases with misrepresenting cartridge designations on the face. In this particular instance, not really a safety issue as if you were to load and fire them in a rifle chambered for 308Win, there would be little if any recoil and the case would fire form back to its original form.