A reinstall from your discs will remove the patch, and you can save your pilot file so that you wont lose your progress. It's been ages since I did anything with FS1, so I don't know whether the patch changes any mission files, but the bug you're hitting almost certainly has to do with the structure of that particular mission, nothing to do with the engine or the way your game is playing. Volition's missions were historically fairly straightforward, and in many instances not heavily stress tested, thus they were (in some cases) easy to inadvertently break, which may have happened here. Someone who has worked on the Port (Goober is probably the best man to speak to) might be able to tell you if they tweaked that mission to prevent this particular bug - if they have, it's probably not too challenging to convert their FS2 mission file into an FS1 mission file which you can use it to progress.
All that being said, however... FS1 is a very old game now - over 15 years - and a lot of technology has changed since then. If you do end up heading back to GoG, I'd strongly recommend getting FS2 and FSOpen in place of FS1 - you can install the port, and never touch the main FS2 campaign or any of the mods, and it will play and look almost exactly like FS1 - you can even set it to FS1's 640x480 resolution if you so desire. The only things that will change that you're likely to notice will be the structure of the Command Briefing window (just the position of the anis, nothing significant) and the nebula BGs. Otherwise, it's effectively identical, but the engine will run flawlessly on modern systems with >2 GB of ram.