I've tried building my own projection matrix both with the above approach and with this one:
Both didn't help. Strange thing is, in both cases only changing the value of FOV changes the result, while near and far plane values seem to be ignored at all.
Why this? Is this kind of matrix / projection the thing I need here at all? Looks to me very much as if I'm missing something incredibly basic, but somehow I couldn't figure out what's wrong here.