Hey Colin,
I don't think you need anything as fancy as a desolder station. Honestly I have found they tend to tear up pads. I have had better luck with an extractor and solder wick.
I have now replaced two headers in TM50x back planes. You just have to go slow and easy. I think it took me maybe 30 min to get them out once I had the PCB out. Both were done the following way.
1) Added a bit of flux with a Kester 951 flux pen
2) Added fresh solder to each pin (I like Kester 245 no clean)
3) Using an Soldapult "sucked out" the solder from each pin. Be sure the solder is fully heated before you engage the pullet.
4) anything that does not fully suck out add fresh solder and try again. Add flux before adding fresh solder.
5) Using a small flat jewelers screwdriver try to wiggle/break free each pin from the hole. Some just need a bit of flat force to break free, some will need you to heat them with an iron while pushing the pin to the middle of the pad at the same time. Some will require you to add solder, Soldapult and try again.
6) If you feel you have all the pins done then slowly pry the connector off from the other side with a flat blade screwdriver. Some pins will not pull, or be stuck and some will start to pull up. Find the "stuck pins" and go back to step 5.
Slowly working through these steps you should be able to get it open. Of course if you totally give up you can use a dremel tool to hack the plastic off leaving just the pins. Then heat each pin, pull out with a tweezers and then remove the solder in the hole with the Soldapult.
This does assume you have a good iron with decent thermal recovery. If you have just a simple once piece irons or one of those cheep Chineese irons it may not have quick enough thermal recovery to get the heat through the pins fast enough before the pads are damaged.
Good luck, it is a pain but worth it, and not that bad once you figure out the technique.
