I would sell the one that you have the least connection to and do not use as much as the other two.
Tikkas are great rifles, but I am confident that you are going to love your new Sako!
At the end of the day, if you have a great 150 or 165 gr load for your 308 and a great 180 or 200/220 gr load for your 30-06, and hunt at reasonable ranges of 400 yards and less, than you will not find that you are missing your 300 Win Mag. And that includes game such as bear, moose and elk. There have been more moose shot with a 303 British and 30-30 Winchester than any two other cartridges in Canada. I would safely say that the 30-06 and 308 would rank right behind those. They are easy to get within range of, and if you find yourself inside 300 yards with your 308 and a 150 or 165 gr bullet, you will not be under-gunned! Place your bullet well in the heart/lung cavity and you will be enjoying moose meat all winter!