Here is how I do in situations like this:

Play the new installation a little and save. Exit game and search for the save and go to its location. Delete that save as you probably care nought for it and move your old saves into there instead. You can filter for files created 'today' as your new save was just made.

If you are on Windows, I strongly suggest to unhide hidden files (but leave the super hidden ones) and untick the "hide extensions for known file types." (However the exact wording went. Makes life easier.

They moved the save files directory to the documents folder IIRC, probably to facilitate any scorched earth solutions to bad installations by having the save games separate from the game directory.

So, after many hours of searching, I tracked down the save files here:

C:\Users\REDACTED\AppData\Roaming\HardLightProductions\FreeSpaceOpen\data\players

Not exactly easy to find, lol!

Now I've got another problem. My old save file is in .PL2 format, but the files in this new location are in pairs of .CSG and .JSON formats. I also note the PL2 file is only 2kb, whereas these 'new' ones add up to 60kb.

Something tells me OpenFS must have been using a multi-file save structure and I've only got part of it. I'd assumed it 'worked' as back then I'd been using it to 'roll back' my progress (ie cheat when I failed a mission) buuuuut obviously I was wrong.

I remember I was up to the point where mission outcomes started to cause branching progress. Any way I can 'skip ahead' to this point on a new file?

Freespace 2 has a linear campaign, there is a string of missions you can opt out of but that's it. The only real variation is the ending and that depends on what you do in the final mission.

Have had a look on the WIKI and I was on either mission 8 or 9 (Into the Sixth Wonder / Into the Maelstrom)

Question remains, is there any way to jump ahead? Anyone have any archived save files or something?

Have you tried at the Hard Light Productions forum?
See if they have a save file editor or something like that.

They don't have a savegame editor, but if you don't care about stats you can play any mission in the game by going to the mission simulator and pressing ctrl+shift+s to display all the missions.