I didn't find any need to remove the pressure contact. I just pried the battery connector up (gently) with a spudger and left the pressure contact in place. Connected the new battery and aligned the pressure contact screw hole. Replaced the screws, finished reassembly and all was good.
Mechanical pencil eraser does work perfectly to press pins. Let's you control the board and the pin with one hand while manipulating the barbs with the other. I found that a straight hemostat worked really well in place of pliers. Squeeze the barbs as near to the end as you can, then push them into the hole until they're wedged. Use your fingers or a spudger to push them the rest of the way through so you don't endanger the logic board with a metal tool. Got all four of mine out and back in intact, all in about five minutes. If the barbs don't break off, there is no danger of the pins flying because of the spring -- they are captive on the heatsink.