I'm wondering if I need to do the lighter fluid thing (or is that not a good idea?) or just re-lubricate it, or what
I think it depends how valuable the shutter is and how keen you are to spend money on it. FWIW, I had a sticky compur shutter in a retina IIIc. I DID do the "lighter fluid thing" (I actually used spray isopropyl alcohol) to flush as much oil as I could from the shutter leaves and mechanism. I then gently lubed the bearings and contact points with a little watch oil. (which are easily exposed) I didn't really know what I was doing, but >1 year on the shutter is still snappy. I don't think the DIY approach risks damaging the shutter particularly. (Don't physically touch the shutter blades other than with the lightest brush) Worst case it ends up back where you started - oiled up, and you have to get it professionally cleaned.