I know I'm stating the obvious, but - have you tried JUST alt-tabbing without minimizing? I'm sure you're minimizing so you can get yourself some space, but I hardly ever minimize games that are windowed myself.

Also Lerend - the funny thing about those so-called anti-cheat measures (I've played numerous Japanese-developed games that have this stupid "feature") is that they do little but to stop casual cheaters. Anyone who can Google and follow directions with technical stuff can easily bypass the full-screen-only requirement, so I don't know why companies continue to do it - as a means of making their investors feel "safe" that their game is "cheat free" thanks to the inability to alt tab?