Presuming the D300 is the same in this regard as the D200, have you tried pushing the little button that pops the card out to make it more accessible? This also has the advantage that the card is already pushed off the pins, so it slides out easily.
Nikkors: 17-55mm f2.8, 18-200mm f3.5-f4.5 VR, 70-300mm f4.5-5.6 VR, 35mm f2, 50mm f1.8, 55mm f2.8 AI-S micro, 105mm f2.8 VR micro
Other Lenses: Tokina 12-24 f4, Tamron 75-300mm f4-5.6 LD macro
Stuff: Nikon SB800, Nikon MBD200, Gitzo 1327 Tripod w/RRS BH-55LR Ballhead, Sekonic L-358 meter