Hmm... I don't really know, but here are a few thoughts.
Putting money in to a 2012 machine may not be wise. I don't know the Mac Mini well enough to even know if that is possible.
You might be able to buy a used machine that is better than what you have for less than $800. If you have a trusted friend who wants to part with such a machine that would be ideal. Next best option, a local Mac repair shop.
You might not even need a Mac. If you're using your machine primarily for basic tasks like email and the web a Chromebook might suffice, which would be substantially cheaper than a new Mac. Modern Chromebooks do much more than email and the web, but power user jobs like video editing are probably still better done on a Mac. You might make a list of your "must have" features and visit a Chromebook forum to see what users say.
Another option could be to think of a new Mac like you would a leased car. Divide the price by however many months of full support Apple provides via whatever support option you choose. So for example an $800 machine plus $300 support divided by 36 months would be $30 per month. When the 36 months is up sell the machine, and buy a new one, thus you're always covered by full support. These numbers are best guesses so you'll need to plug in the correct numbers of course. If you put the new machine on a credit card then you can pay per month, with interest added to the price of course.
All that said, I'm a bit surprised your 2012 machine is having such limitations as I'm on a 2011 iMac and not having such troubles. I suppose there could be something wrong with your system software, which would be good, as that could be fixed at no expense.
If you have an external drive you could SuperDuper your entire setup to the external drive for safe keeping, and then do whatever repairs on your boot drive that you decide are necessary. If the upgrade goes wrong, you still have your current setup available.
