The 1-12 twist rate will not support a heavier bullet. You are correct in wanting to go with a 1-10 or a 1-9 twist rate, especially for coyote hunting. Squirrels will die, no matter what you hit them with (given proper shot placement). .223 is going to be a better caliber than .17 HMR for your purposes due to the cost of ammunition. .223 also has a longer range capability and a wider selection of bullets available. Nosler, Hornady, and Remington all put out excellent bullets for that caliber. I have the most experience with the Nosler Ballistic Tips and Partitions. The cost difference between the CZ and Tikka is somewhere from $100 to $200 depending on the dealer. Here is a comparison list for you:
Tikka:
Lighter Rifle, 1 MOA or less guarantee out of the box, Removable flush fitting magazine (plastic), $100-200 more expensive, lighter in weight, comes with 1" scope rings, have to deal with Beretta for servicing, very smooth bolt system, more expensive "accessories," synthetic only stock, available in blued or stainless, no iron sights.
CZ 527 American: Hammer forged barrel, comes with scope rings, 5 round capacity mags only, no iron sights, blued barrel only, no MOA guarantee, heavier rifle (less perceived recoil), mauser style action, walnut stock only, very strong action, $100-200 less in cost, less expensive "accessories," deal directly with CZ manufacture (good customer service).
My own opinion, selling both for about six months in a gun shop, comes down to style and preference. They are both excellent guns. If you plan on carrying it for a long distance, the Tikka wins out, if you are benchresting, the CZ is better. Either way you go, you win. Good luck and happy hunting.