Ran into this a number of times with Savage actions, barrels and nuts. Usually it was a matter of the barrel pointing off to one side, but I did have instances where it pointed essentially straight up, or straight down, which really messed with the elevation zero.
The tolerance stacking between the factory barrel threads, the receiver, the barrel nut, and the recoil lug, combined with where the headspace gauge puts everything, affects how the barrel 'times' relative to the action. Most barrels are not arrow-straight, as the saying goes. Good gunsmiths can and do time what curve a barrel has relative to the receiver to minimize this effect. With the barrel nut setup, there isn't any gunsmith involvement, and no way to really change the timing.
I will say that using the barrel nut and recoil lugs from Northland Shooter's Supply cut this sort of shenanigans down to a minimum, at least in my experience. The amount of difference compared to using the factory nuts and lugs, even the ones found on the 'target' actions, has to be experienced to believe.
Before that, the solution that I used for a lot of years was to invest in the Burris Signature 'Zee' rings, with the plastic inserts. They come in sets of 0, 10, 20 and even 30's. The idea being that with the '0' inserts front and back to float the tube you don't end up with the rings pinching the scope tube and inhibiting any internal movement. If you need more elevation, you can put say, a set of 10's in the rear, with the +10 half on bottom and the -10 half on the top, to tip the scope forward/down a little, and gain some additional range of travel. Need more? Either swap out the 10 in the rear for a 20, or swap the 0 in the front for another 10, but flipped over. Between the different values, you can get a *lot* of range of adjustment. Or, as was often the case for me, you can put a set in *sideways* to make up for a barrel that is pointing off to one side and eating up all your windage adjustment in your scope.
It's my opinion that Burris originally made these because frankly, back then, their scopes sucked balls and had crap for range of adjustment. Like 20-25 moa, total. Ridiculous. But it was a life saver for me, back in the day shooting FTR with a factory Savage and 155 gn bullets. I needed *all* the windage available on the NF BR & NXS 12-42x scopes we all ran back then (all whopping 45 moa of it), especially on the ranges I frequented. Given that as you crank the elevation and get further from mechanical center, your available windage adjustments goes down as well, it was real easy to get into a bind - literally. I've done it, and seen others do it as well - put on 32 moa of elevation, then crank on 10 moa of windage. No problem. then crank on another 5... still okay. Go to crank on more... and suddenly your elevation takes a dive, as the inner scope tube runs into the outer (for lack of a better description) and follows the curve. People frequently thought they broke their scope, until they took everything back to center and it worked just fine.
Anywho, that's my opinion on what you have going on. You can either swap scope rings, or change the barrel nut and recoil lug, or both.