Thanks for the data. I shoot Remington Core-Lokt bullets almost exclusively. They are cheap and at the ranges I shoot (always well under 200') they are accurate enough for me. I shoot the 150g in my .308's. I use the 180g in my 30-06's. But, your data pretty much confirms my typical practice with the .308 and 30-06 sighting in at about 1" high at 100'.
Try 165's and see if your groups don't tighten.
I don't expect a light gun to shoot the same when the barrel is hot. It's Ok because you're only going to need 1 shot anyway. Or ....most likely, you're only going to get 1 shot.
Every .308 cal. gun (30.06 included) I have ever owned, likes 165 grain ammo. I have never been able to get 150's or 180's (forget 200 -220") to group. The old adage that the 30.06 is versatile is only true if your hand loading and then it's a stretch.
You said that the gun shot well once so it shoots well. You just need to find out what it shoots well. You've got this much time into it, I suggest you get a box of these,(
Graf & Sons - HRN AMMO 308 WIN 168gr A-MAX MATCH 20/BX 10/CS) sight the gun in as Eddie Walker suggested, (That's the way I do it), The barrel should be ambient temp before every shot, Do not shoot past 50 yards unless your have your group under 2 inches.
This shouldn't take but around 5-7 rounds, so use the rest of the ammo when sighting in the old scope that you took off.... if this doesn't work.
look around the peripheral of the scope from the objective end, as if you were using it to view something, only instead of looking through it, look up at the inside of the tube, look for cracks or facets in the glass. When the scope of off the gun put it in the frig and see if it fogs when you take it out, on the inside of the glass.
If this doesn't work it's the gun or the scope, most likely the scope, as the gun shot well with the other scope.