I wouldn't just haul off and throw money at the problem. The issues described on the Hornady website don't really explain what you're experiencing. For one thing, you're talking about a 20'' barrel, which has plenty of impingement and dwell time. That barrel and gas system gives you more than enough time for pressures to drop well below what you need for safe extraction. You can expect to experience increased bolt velocity when using the suppressor, but I don't see any way use of the suppressor explains popped primers or short stroking.
If you are in fact experiencing short stroking, then I see no way an adjustable gas block can help you in any way. All it does is mimic a smaller gas port, which is going to make any short stroking even worse. If however the bolt is going too fast, as I suspect, then an adjustable gas block is the cure. Or a heavier buffer might also work and may be cheaper. Again, what in detail is happening that makes you automatically assume it's short stroking?
At the very least, I would use some regular factory loaded ammunition. There's just no way in my mind that a suppressor on a 20'' barrel could be the cause of popped primers.
ETA: If we were talking about a 12'' barrel then maybe I could see the suppressor causing popped primers, but certainly not short stroking. On a 20'' barrel I just think that the pressure has dropped so much by the time the bullet actually gets to the suppressor that there's really not much the suppressor can do at that point to cause you any extraction problems.
My best guess at this point is that your rifle is already somewhat overgassed and the suppressor is just sending it over the edge of what your magazine spring can keep up with. But again, that doesn't explain the popped primers in my mind. I would strongly advise you to try some factory ammo just to eliminate a variable and see what happens.