OMG! It is entirely possible to both remove and replace the MagSafe Connector without removing the logic board, making this 5 or 6 steps instead of 33!!
Once you remove the lower case (and disconnect the battery if you feel you must—I’ve been inside my MacBook a dozen times and no longer find that necessary, although it probably is safer to disconnect it), you can skip skip straight to Step 28 and remove the display data cable. Move that out of way and remove the two screws securing the MagSafe Connector.
Now, with a little finesse you can lift the MagSafe board and slide its connector out of the logic board. I nudged it out a bit with a screwdriver from the part that was visible (on the other side of the logic board) and gently pulled the five wires and it slid right out. It didn’t put any stress on the wires at all.
To give myself some wiggle room I also removed:
one screw from step 30 (5.2 mm Raised Head T5 Torx screw)
two screws from step 16 (4.4 mm T5 Torx screw and 5.0 mm T5 Torx screw with 2 mm collar)