Contact support. Be as much detailed as you can about the problem, and in what machine you're trying to play (your OS, graphics card, processor, etc).
If their suggestions doesn't work, you can have your money back.
More info: https://www.gog.com/support/support_view/30_day_money_back_guarantee_faq#en

experimenting with slime ranching, I guess? I imagine it was a way to reintroduce butchery in the game (the dev cut it out of the game because he was unconfortable with it), without actually killing cute farm animals.

I know some people use it to farm irridium by herding and then killing some specific types of slimes.

My wife keeps hitting me up about it.

So that's another point for you : pleasing your wife. Herding and then maniacly slaughtering cute little slimes is just a bonus ^^
Wants to be a slime rancher... Abby (loves creepy stuff) or Maru (for mad scientist purpose), I guess?

It's Abby but I'm not building one .....yet. I give that woman gifts every other day; she should be happy for now. :P

I got the Statue of Perfection.

Can I get on with my life now? :P

Does the game have any finish-able plot that can eventually be completed (think something like reuniting your family in "Sid Meier's Pirates!" for example) or is it just the sandbox stuff and/or upgrading your farm and that's it?

After, I think three years, your grandfather's ghost shows up and gives you a grade. If you score perfectly he gives you a statue that makes the really valuable ore. If not he gives you a chance to improve, though I totally forget how this is implemented.

I'd say you "finish the plotline" when you complete the community center and get married and kids. Both give you a kind of conclusion (saving the town and building yourself a new life).

OR fuck the Community Center, side with JoJo and make a mint. ;P