Well, accuracy comes before capacity. Right?
I say ditch the magazine and convert to single shot, if this is needed to hit your mark.
My groups at 100 yds are < 1". This is just starting out with a new rifle. This is with some Sierra GK's that I'm using to break in the barrel.
Not as good as some on here, but I don't see that as a reason to switch to a single shot.
I'm trying to get the best accuracy, but it is my hunting rifle so I'll be using the magazine all the time.
Yes this is normal. With a lot of rifles it can be a challenge to reach the lands and still fit in a DBM. I don't own Tikka but own lots of Savages with DBM.
Lots of times, you don't need to get .10 off the lands. Something like .20 to .25 can often work great. So play around with the seating depth a bit and see what really works best. Sierra GM usually are not too sensitive to seating depth. You may just be able to set them to max you can fit in the DBM and they will work just fine.
What are you using the rifle for? Are you going to work on it for competitive shoots? Do a stock or barrel swap? Get the action worked on? Or will it be used for hunting and the pleasures for just going out and shooting? I can see if it was for competition, then if needed make it a single shot, but if not, then i would back it off some, .20-.30, so they will fit. You will still get great accuracy from that Tikka, sub MOA all day with the right combo.
Now if you REALLY mean't that your priority is to use a DBM, but would like to get the best accuracy you can get despite, then I say do seating tests during load development within the range accommodated by the DBM. If the best you get is ~1moa then that's the best you get -given the constraints. You're as likely to find better accuracy with any luck.
I know I come off as a smarta$$, but I think you would be amazed by the power of single accurate shots. It's atleast worth testing for to consider.