Computer is smarter than I am today...
So to repeat, how are you crimping? That seater die has no crimping function. If you are not crimping AT ALL I would strongly recommend that you try it. The difference it makes by evening out the starting pressure (pressure at which the bullet begins moving in the case mouth as it starts to head up the bore) can be surprising. Remember this - accuracy requires consistency. Learn to be consistent one step at a time, both loading and shooting, and you'll be tearing out bullseyes in no time.
Also since you have a good quality seater, have you checked if the seating stem in it matches the profile of your bullets? They're generally pretty flexible in handling most bullets until you get into the very long-for-caliber, low-drag bullets we see everywhere nowadays. The longer your bullet is, the greater your chance of accidentally creating lateral runout and/or uneven neck tension if the seating stem and the bullet don't work together well. And if you have a polymer-tipped bullet the possibility of deforming the tip while seating goes off the charts if the wrong seating stem is used. That can turn a tack-driver load into a "***" in a heartbeat!
With your seater I suspect that lateral runout is not a huge issue, but it doesn't take much pressure to almost microscopically deform the case mouth if the first contact with the bullet is out of alignment. Crimping also serves two other key functions - 1) to help correct any accidental deformation of the case mouth, and 2) it serves to increase the overall holding tension on the bullet, so that it doesn't move under recoil while in the magazine of your rifle. Even a 30-06 has enough recoil to cause uncrimped bullets to move in or out the case mouth when sitting in the magazine, and the lighter your rifle the more recoil those rounds get hit with. If the bullet moves, seating depth changes from round to round... even by a few thousandths of an inch...you guessed it, inconsistency = inaccuracy.
Pretty easy to check if your bullets are moving under recoil...say your magazine holds 3 rounds. Measure the overall length of two rounds to the thousandth, writing it on the side of each case in marker. Load these two first. Put a third round above them in the mag, and chamber a 4th round before inserting the magazine. Pop the mag in, and send two rounds downrange. I would measure/mark about 4-6 rounds and repeat this procedure 2-3 times, WITHOUT shooting the marked rounds. Now, after each measured/marked round has been hit twice with recoil, re-measure the overall length, and BTW inspect the tips to see if they look any different than they did before you loaded them into the magazine. If the overall cartridge length of any marked round has changed, you have either bullet slip under recoil due to insufficient neck tension or the rounds being battered due to the entire cartridge moving inside the magazine, again from the rifle's recoil. Tikka's are light and well-balanced but that light weight does come with its price - greater felt recoil. Your rounds in the magazine are hit with just as much force as you are on every shot.
Recoil can also affect the powder arrangement inside a cartridge, which theoretically could affect accuracy. But in a 30-06 with 4350 or Varget...that one's really a stretch unless for some reason you were fooling around with reduced loads (wrong powders for that!) or (GOD FORBID!) mixing powders.