What kind of rings are those?

You say the first two almost touch. Try shooting 1 shot every 15 minuets for a group and see if heat is causing it. If it's moving when it heats up any amount , then either the action or barrel is stressed. Likely that pressure bump in the barrel channel is causing all your trouble.

Leupold dovetail rings

First thing I thought of to.

thry some flat based bullets like power shoks. my tikka was a new day with flat based.

Both my Remington's love hornady super performance. SST bullets are great for deer as well. Good luck!!

I can definitely attest that a hot bore will throw off accuracy. It can happen with any rifle too. I learned the hard way after sending shell after shell down range with inconsistency. I finally had the range master tell me I may want to let the barrel cool off a little. I put it in front of the fan and shot 3/4 inch groups afterwards.

Also, tap the adjustments on the scope after setting them.

Dr. B

I've been considering purchasing a new sythetic stock for this gun. Any suggestion of what stock to buy before I do any work to it?

Don't mess with that pretty gun!

To the right usually means a slight trigger jerk or a flinch
back to square one...ear muffs and get a lead sled...

Most of the hunting rifles I've shot you only get three shots before the heat of the barrel starts to change the point of impact.