the specs IIRC allow for a 0.0155 thick brass at the neck
if you add 0.031 to 0.284 you get 0.315, so you would have to remove brass from the necks, perhaps up to 0.007 to match the diameter spec'd
what may be easier, is to lube them, then run then into 0.280/0.281 sizing die, and push then in finger snug in an fired/NON-resized case, load and shoot
I have to wonder if you could even get them to seat without expanding to 0.280 or more, unless they are hard.
also, another issue is most, if not all 7mm cast moulds drop fatter than 0.284, more like 0.286
I'd say, unless you want to dedicate some brass and have very thin necks, the drawing of the bullet would be your first road of travel.
Edit to add: just check SAAMI specs, and the neck is designed to allow 0.0008 for expansion.... not near enough without taking off a lot of brass.... 0.3150 - 0.3088 = 0.0062/2 = 0.0031 brass removal to get a TIGHT fit... you'd have to remove a bit more to allow chambering.