Smoke, been an AR armorer since 64. If you are loading a single round in the mag then trying to chamber that round by closing an open bolt, 98% of the time it is a magazine problem.
The AR 308 has several versions using different mags. The AR-10 is an Armalite and mostly takes M-14 mags except the very early version the upper has a 45 degree angle at the rear bottom ending at the takedown pin hole.
The DPMS has at least two different versions or generations they are supposed to use Pmags but..... the upper has a rounded back, the bottom ends about 1 inch behind the takedown pin hole. The LAR by Rock River is another matter it is prepritory and has a different length bolt and upper.
If you have a mag that locks into your lower and will start to feed, I would try turning the front of the mag lips down a little, length wise using a pair of needle nose pliers from the front, with a twisting motion to the inside, both sides evenly, until the round goes right into the chamber, a round nose might help. Adjust the lips a little at a time until you get the bullet's nose down a tad so it feeds. Your description is of a straight wall case bullet nose coming up too fast. Nose in chamber top, case base still in mag.
Look where the case mouth is when it jams, if it is off to the left a bit, bend the left lip in a bit more to bring the bullet to center, if off to the right bend the right lip in.
This is cheaper than buying another mag, just do not gorilla the mag lips, go easy, a little at a time.
When you get it right it will make a sound you will remember from then on. Sort of a zoomph sound.
Make a dummy round for this process, no primer or powder....
Ed