Good morning Mr. Miller!!
STAY THE COARSE, I think your SPOT ON!!

I have bought a half dozen rifles that "wouldn't shoot".
One worked out to be one of my most accurate rifles,
It was a Howa 25-06 with a huge 6x18 Simmons scope. EXACTLY like yours, I found loose bases AND a bad scope. I sent it to Simmons and they credited me more than half on any scope in there line. I took a Whitetail series with the "granett" finish. Works perfect now, shoots 1/2" with off the shelf Winchester 120 ptp ammo. I gave it to my brother.
Another was a Ultra 30-06 Handi rifle. It too would not group AND popped open. The scope was fine, but again the base was not properly mounted AND the shelf was oil coated and filthy. I cleaned it up, re mounted the base and scope and I have another good shooter H&R.
The last that comes to mind is a beautifully stocked Argentine Mauser. Now I have built four of these myself and this one looks just like one of mine sans the wood stock. I have used synthetic every time. This one was a 280 with a old M8 Gold Ring 6X Leupold scope. Again the scope was at fault, because the rings where bad. They where slightly off center, causing the scope to go to the xtream in windage adjustment. Well the old Leupold's used a different designed reticule back in the '60's and this was a weak point. I sent it back to Leupold, they fixed the scope for free and I installed Burris rings and NO MORE PROBLEMS!
I have worked with Gun Smiths for over 20 years and I can honestly tell you, scope bases, rings and the scopes them selves are THE TOP ACCURACY KILLERS!!!! EASY work for a GC and its fixed!
Best of luck, your on coarse to fixing yours!
CW