Just a few thoughts, purely FWIW & in case it might be useful to anyone. I apologize Dragonlair because none of this is really meant to help with your problem -- Chris is already doing great with that. My goal is to add to the amount of useful info Chris has already posted in case it helps someone going through this thread someday.
While I don't disagree with: "Yeah, a VM isn't really the right solution for the handful of games you've got left and there's no guarantee that the problem games would even run correctly in a VM.", to me the key there is running a VM on a laptop, unless you've got one of the desktop replacement rigs.
I prefer VirtualBox, which has some pretty decent regular & beta graphics emulations. On a desktop with a 4-8 core CPU that supports virtualization in hardware & with enough RAM that you can increase the allotted memory along with CPU cores, I'd expect that you could run probably 99% of the so-called casual games out there [and probably quite a few other types of games]. Doing so would of course be for convenience, such as not having to worry about your regular desktop getting rearranged or re-sized & being able to pause the game & do something else -- alt-tab is in my experience pretty twitchy with these.
From what I've seen so far win10 might be a great choice for games in a VM -- better graphics & graphics ram handling should lower the bar on host system hardware requirements, & some people are reporting 10-15% game performance increases in 10 vs. 7/8.1. That said, I'm not sure upgrading 8.1 laptops is always going to be fun. Like tablets, many laptop models are limited production runs contracted to whatever Chinese/Taiwanese company. Some of the hardware components may be more generic, with updated driver files impossible or near impossible to come by. I've also seen reports that on some laptops win10 will not perform an upgrade -- you have to wipe the disk & install fresh.
That all said, graphics driver availability *may* be increasing for laptops & tablets. IMHO higher demand for more standardized hardware that can be more-or-less plugged in with other components may be leading to less balkanization of drivers. The idea is that whomever assembles the tablet or laptop does much less engineering, keeping costs down. And as keeping costs down is the goal, offering updated drivers when they become available is getting more rare, unless they fix a particular problem with that model.
Apps like Speccy may help -- looking at current graphics drivers can help -- but it can take a bit of work with Google before you find a newer graphics driver for your hardware [it took me about an hour to come up with the graphics driver page for the Intel SOC my tablet uses]. Wherever you get a graphics driver I recommend a full disk/partition image backup 1st. It also does not hurt to read forums on graphics drivers... there's undoubtedly a lot of junk & chatter to wade through, but occasionally it can be worth it, e.g. when an old drivers needs to be completely removed 1st.
There may be other files that need updated at the same time -- many tablets & laptops increase battery life by limiting graphics hardware features &/or horsepower, that's restored when the system detects it's plugged in. If new graphics drivers don't work properly with old power management &/or battery related software, you can see where that might be a problem.