Well, I learned a thing or two today, unfortunately, with little success. I'm going to list all my steps here hoping it saves someone time.
Unibeast install went fine with no special tricks required, then got the endlessly spinning wheel upon reboot, which I somewhat expected... successfully rebooted into safe mode, ran Multibeast with normal settings for my board per another thread here and messed with Chameleon Wizard for some time, managed to inject the first string, rebooted and got a white screen with checkerboard effect on top left... safe mode again, injected the 2nd string, which messed up the system to the point that it wouldn't even load in safe mode... reinstalled the system, booted in safe mode again, Chameleon Wizard in every combination of MacMini6.1 and 6.2 and strings 1, 3 and 4, rebooting after each one. Strings 3 and 4 seem almost there, the screen flickers as if trying to load, but then goes white with checkerboard on top left, or completely black with only the mouse pointer visible.
Interestingly, everything works fine in safe mode after injecting, the System Profile identifies my cpu as i3-3220, and the graphics processor as HD 4000. Seems that I'm very close to success, but as it's now 4am where I live, I guess I better give it a pause. Help is desperately needed.