In case this is helpful,
I just recently desoldered the backpack on my display using just a soldering iron.
First off the backpack had slight corrosion on some of the pads probably from whatever flux SF uses to attach the board. That kinda bothered me. Also the backpack was mounted slightly crooked.
I decided to put connectors on the two devices.
I use a 800 degree F tip to do all of my soldering, so that would make a big difference when attempting this.
I used masking tape to protect the display from flying flux.
I use isopropyl alcohol to clean my boards afterward, but I couldn’t dunk the display like I normally do, so the tape helped.
I held the display elevated above the bench so gravity would pull the backpack away from the board when it was ready.
(I thought it would just fall but the connector holes on the backpack aren’t a complete match to the display holes)
(The connector is 11 x 2. The 11’s axis pitch was correct but the 2’s axis is off.)
I gobbed on the solder and went back and forth a couple times till the backpack tilted and then I slowly pulled it away from the display. Taking the pins out of the packpack was pretty easy. Almost the same method except I used pliers on individual pins.
Then I used a solder sucker to open the holes. (The spring activated type)
Solder the new connectors using the boards as guides (remember, the holes are wrong, so there are small angles to consider.)
I cleaned the display by soaking the connector side in alcohol for 10-15 mins and slowly brushing the area with a toothbrush. Display was only as deep as the connector!!! (No alcohol on the display area!!)
Also, if you need to program the board without removing it, you can use those ‘pogo’ pins…
Dave