I just had the same trouble with my center console. I wound up pulling one of the screws out of it's anchor. Actually, it may have been loose to being with as the whole thing has always felt loose to me. I think the whole piece is really a poor design. The back screws should be on the side, it should make better use of space, have cup holders, and have better protection from dirt and stuff.
Are all these center pieces the same? Mine has a box with a flip-top lid and 6 switch locations surrounding the base of the e-brake. There's a bunch of empty space between the bottom of the box and the floor of the truck. I'm wondering if there might be a better design out there that I would like better. I have an AT, and I guess the one for MT would have a different cut-out for the shifter.