Identify the main harness that connector is part of, then unplug all the other connectors that share that same harness.
Push the harness and connectors all the way down into the lower cab.
Raise the playfield, and pull the disconnected harness out. You should be able to handle the defective connector more easily.
Whether this is less overall effort than disassembling the light panel and other connectors, depends on the particular harness, etc, so it's your call there.