How to remove press fit connectors

I'm trying to repair an arcade PCB with intermittent audio. The board on top is the audio board, the bottom board is the everything else.

There is a short or poor connection somewhere in this 96 pin DIN, press-fit connector.

I have OEM replacements, and would like to install new ones, but really have no idea how to do it properly (if you can even do it properly). My first thought was to do the following:

• Physically cut the pressfit connection to remove the plastic housings
• individually remove each cut pin from the PCB
• 3D print a "frame" around the connector area to minimize PCB flex, and use an arbor press to insert the press-fit connector

If anyone else has suggestions, I'm all ears!