.416 Ruger is .30-06 length. I once upon a time, had a .495 A-Square on a Sako action (a cousin to the Tikka?), so the ability of the steel to withstand the bolt thrust I think is nothing to worry about. That is why the SAAMI spec stuff governs the industry - to protect everyone.
A 1938 Mauser could be used as well. You haven't shared what the quarry will be, however, a .416 will likely be used at some point for a critter that can bite/stomp back. Controlled round feed is where my comfort zone lies for this type of hunting. Sure, you would be backed up by your PH, who undoubtedly will have a CRF rifle. I chose to have my own reliability/redundancy via a Ruger Alaskan. I have the .375 and .416 Ruger versions. The .416 Ruger shoots 5 round, sub-minute groups at 100 yards, BTW. I do find that for me that the .416 at 2333 FPS with 400 gr projos, is pegging my recoil tolerance. Dr. Robertson has counseled me to relax that down to 2100 - 2150FPS, but I have not had a chance to try his Rx. If you try to chase the pressure limit, you may need to use an A-Square style stock to mitigate the perceived recoil - depends on your personal recoil tolerance.
This goes off course for your Tikka action question, but wanted to bring it up in case you were unaware. I think Tikka makes good rifles (I want one myself), so do what makes your Goldilocks rifle dashboard light come on for you.