How many rounds do you have out of that 30-378? I would be willing to bet it doesn't have much life left if you have had several iterations of 200-250 rounds, a shot out barrel can send flyers that look like a POI shift.. But yes I agree it's probably a combination of the barrel being "too" clean and being tense before your first shot. Try not using a bore brush if your use one. Try Hoppes no. 9 wet patch a few times, let it sit for 20mins, dry patch, oil, dry patch, ever 120-150 rounds, and see what that does with your POI. This should make it so 1-2 fouling shots will have you on the money, and your first shot will still be very close. Many other cleaners are too aggressive and clean the barrel to way too much, so that the conditions within the bore are dramatically different from 1st shot to last before cleaning. Definitely listen to the "cold bore" zero" and dry fire advice up above if you want that first shot perfection.
Just my 2 cents