Long story short...

I recently purchased a small hobby-business that belonged to my friend.
He died unexpectedly in April. His family and I got all of the legalities straightened out so that everything is now in my name.

Pair Networks is the current hosting company and PairNIC is the domain registrar (same company). In my opinion, both are very much overpriced.

Everything is pre-paid through December 31st. I would like to dump Pair by the end of the month so that I can be credited the final 2 months. How can I pull this off?

If everything's pre-paid why do you want to have money back? As far as I understand you're a noob and don't know a lot of things anout this business. You think if you have a cheap hosting you'll not have issues with it, don't you? I can assure you not. You know "you get what you pay for". Cheap hosting means low quality service and bad support and downtime, etc.
But if you still want to change your hosting you have to find the new one, buy the necessary package plan then change your DNS at the registrar (your site not to have outage) and then leave your previous hosting.
Good luck.

Pair Networks is a very reputed hosting company. Do you have any hosting problems with pair? Unless your business can not afford to spend a hosting amount, it is recommended not to change the host without studying the problem further.

There are others web hosts, that offer terabytes of bandwidth for a small price. But, in practice, you find that they provide very limited server resources and glad to close the accounts of those who use server resources beyond planned levels (this is very different from what they advertise).

You will find some useful threads in DP about hosting.