Alright, I managed to fix the issue and have successfully uninstalled Plastic SCM from my PC now.
For anyone else who might encounter this problem with their own uninstall, this is what I did.
Go into whatever folder you have installed your Plastic SCM into and delete the uninstall file (which to me was appearing as a .dat file, not an application or an .exe).
I don't know if deleting that is truly necessary, but that is what I did beforehand.
Next, launch an installer application for Plastic SCM and re-install Plastic SCM on your computer (making sure to tell it yes when it asks if you want to "replace your existing installed version of Plastic"). Then, the last part, do not agree to restart you computer after install. Instead, go immediately to your Plastic SCM's main folder again (where you installed it to), and you should now see the uninstaller as an application you can actually launch (or at least I did, and I have tested this method twice).
After it (hopefully) completes the uninstall process. Then you can agree to restart your computer, but only when promoted by the uninstaller application at finish. After that, there should be more no more Plastic processes running in the background of your task manager, and Plastic SCM should no longer appear on your computer as either an application to launch nor a program to uninstall in Add/Remove.
Probably the PlasticSCM5 folder will still be somewhere on your computer, but you can just find that in your C:\Program FIles\PlasticSCM5 (or wherever you installed it) and you should be able to safely delete that folder for extra measure.