Some good info listed in here, but I did not see mention of setting your sizing die. I have not sized 308 to 7-08 yet, but I have done lots of 30-30 to 7-30 waters, 06 to 270, etc.
I set my sizing die so the brass fits my chamber. When taking 308 brass down to 7-08, I would partially size the neck and check to see how the empty brass fits in the chamber. If neck is partially sized, you should have a false shoulder. This should keep your action from closing. Keep adjusting your die down and adjusting that false shoulder down the neck until your action just closes with a firm/crisp motion. This false shoulder will adjust your brass headspace and allow you to blow out the shoulder to fit your chamber.
You said you dropped 1.5-2 grains below max. Is this rifle max, or pistol max? Rifles use a slower burning powder than pistols. they have a longer barrel to burn it up. With your shorter barrel, you will likely not even burn up all of the powder from a rifle load and you will leave all of that residue in your bore or flashing out the end of the barrel.
Hotter does NOT = better. Most of my pistol loads are below max because I am not looking for speed, I am looking for accuracy, dependability, and opportunity for taming recoil. I start with the lower velocity and work up into the accuracy. With 7-08, I would likely look into loads with XMP5744, AA2460, H335 or similar burning rates. I wouldn't drop 1.5-2 grains below max, I would start at the bottom of the pistol charts, and work up in 1 grain increments. When groups start tightening, then into .5 or less increments.
I have no rifle or pistol load with a bullet touching the lands. I do have a few bore rider cast bullets that are up in the lands, but the driving bands are not touching. I always leave a .010 to .015 jump for the bullet (unless my barrel throat is long and bullets are short).
Some people load with the bullet into the lands to increase pressure when fireforming brass. In this instance, if you have set your sizing die to make that false shoulder, that will hold your brass and you can seat the bullet propperly.
If you have primers popping out, crush the brass with pliers and discard.
Good Luck and stay safe.
Steve