Okay.... everyone has Tikka's, including me.
From what I've seen these have minimum dimension chambers, and won't accept fired cases from any other rifle including Steyr, Remington, Sako, AI, and other makes. Believe me I've tried this in several calibres to avoid the chore of resizing. Tikka's are tight.
I got hard chambering in my M595 .243 after full length resizing with the Lee FLRSZ die when the press ram was set to cam over. I thought that in this situation there could be some flex in the linkage, and cases which had expanded more might not be being resized as much as the others needing less effort. All my dies including Lyman and RCBS are set up to bottom on the shellholder at only three quarters of the available press stroke.... that's with a RCBS Rockchucker. None of my Tikka's will take once-fired cases unless they're Maximum resized, and then they're neck-sized only.
My only other thought is to try a different brand of shellholder, as some have shallower top sections than others. The case will go further into the FLRSZ die, and allow more of the pressure ring area to be squeezed back down. A few thousandth's reduction could make all the difference here.