I have a Win 8 PC that easily meets the minimum requirements to run this game. Thing is, the frame rate is really bad. I contacted GOG and tried everything they suggested. My Graphics drivers are up to date, I've excluded it from virus scans, tried running it as an administrator, - the works. Still, I have a poor frame-rate.

To give an idea of my setup: My PC is by no means a good one for running high-end modern games, but suits my needs just fine for playing old games and most modern, relatively low-tech indie titles.
I can run the likes of Far Cry 1 maxed out and with a solid - if unspectacular - but perfectly playable frame-rate, but this... no way.

The best I can achieve fps-wise with this game is (and this is an educated guess) what seems to me like below 20fps. This can only be achieved using the lowest resolution and running the game in Compatibility Mode for Win XP. It's just too sluggish to feel enjoyable and the judder makes me feel queasy, honestly. No good.

Can anyone please help?

I'm not sure you are still playing but try disabling visual themes, desktop composition and high DPI scaling. For some reason one or two of these seem to help for Win8 users but as a Win7 users I disable them by default just in case since I don't need those options in-game anyway.