Spike -
Howdy !
I  DK what ranges you might be shooting groundhog & coyote etc in  MI ?
For NE Indiana groundhogs,  I first tried  factory and custom .22-250s, but felt a little under served on deliverable enegry, when shooting 55gr varmint bullets from a  24"  1-14;  w/  practical range limit of 500yd.
For me, the answer was  my wildcat .22-35 Remington, which gave me my minimum desired 450ft lb of deliverable energy out to further distances.   The .22-35 is pretty much  a " .22 Creedmoor ", as regards case capacity; but designed 3 decades earlier.  Cases of this capacity range can give good barrel life, provided you use sensible load choices, control rapid fire rates; and use good cleaning practices.   They can also get a lot done, when fired from a 24-26" barrel.
These days, your cartridge choice might be influenced by primer availability.  SR primers seem to become
un-obtainium before LR primers do.    That might persuade one away from cases that only come set-up for SR primers.
If you don't' slave yourself to an AR platform / magazines, and also are not averse to shooting a single shot bolt gun;   things  become pretty much catre' blance.
I myself don't think one would have to go much heavier than 73-75gr in .224" cal  for a Midwest varmint rifle.
The breezes are not quite like the winds encountered further West in the U.S.  In cases capacities like the .22-35Remington,  .22-250AI, and .22 Creedmoor..... these bullet weights in a long 1-8  or  1.75 barrel can give you a 1,000yd capability.
With regards,
                        357Mag