Not a slight at anybody here and I have no idea as to your - or other member capabilities on game from 400 on out, but it has been and still is my personal observation/opinion, that for big game hunting, most persons should restrict themselves to 350 to 400 at a maximum, and try stalking within range a whole lot harder than some efforts I have seen over the years. A lot more game would be killed properly and fewer would run off wounded.
Would a 30/06 do the job? Sure it would, as will many cartridges with similar ballistics, but that said, would anybody be so ####-sure they would try that stunt on a trophy grizzly bear for example? Moose are pretty much sissies when hit and do not go too far so it is not much of a job to follow up to get them if wounded...but I have had the dubious honors of tracking and killing a fair number big game including grizzly bear that people shot at over excessively far range and screwed things up, then were afraid to follow up on.
I have killed one or more of every animal in North America with a 30/06 and feel confident with one in hand. As far as the Tikka goes, I would not hesitate on buying one, but by far I would prefer the Sako Finnlight to the Tikka. For most of my hunting as well as on the job with the 30/06 I used ordinary Speer 180 grain spitzer bullets handloaded in Winchester brass with cci primers. The rifle I used most was a standard weight pre-64 model 70 and later the featherweight model followed by the Sako.
Both the Winchesters would shoot all day into 1 MOA, while the Sako was better by far, and like my other Sakos in .243 and .308 can shoot 5 shots into a ragged hole at 200 meters. I used a 4X Leupold on the Wins for years while at work and all these rifles now sport 3.5 to 10 variable in Leupolds while one Sako carries a Nightforce scope.
One famous guide-outfitter from northern BC once answered my question as to what caliber he preferred. He said "Who needs anything but a 30/06?" Given that he hunted all over the world, killing everything from dik diks to bengal tigers, lions and and cape buffalo with the 30/06, I think his experience shaped my opinions on the topic. That being said, I am hardly tied to one caliber, just that my preferences change from time to time.