You need some long pliers or forceps...and lots of patience.
Use the F-holes to help you get at the jack. No, you don't need to remove the PU.
Unscrew the jack, let it drop, grab the wires with something and pull them out the F-hole.
Solder them back on, then drop the wires and jack back into the body.
Flip the guitar around and use whatever you can to get the jack back through the hole.
You might be able to use some fine copper wire to secure the jack BEFORE you drop it into the body...then use that wire to pull it back up after you've done the soldering.
In some cases, if the leads are short coming from the pots...you may have to drop all the pots too, and pull out the entire harness through the F-holes....a REAL PITA.
I've done it a couple of times....it's doable, just can be tricky and time consuming.