Thanks everyone, I got a Micro-Mesh kit and the lid is shinier than it's ever been. It had a huge scratch on the far right-hand side of the lid (possibly transport damage), I used quite coarse sandpaper to get rid of that first, and subsequently got onto polishing the lid.
It might need another pass since it's not 100% clear, but it's a perfect mirror finish now. I do need to sort out the lid hinge now, I seem to have lost the little rollers that guide the spring along the lid, and I need to be very careful as the plexiglass hinge supports on the lid are easy to damage (they tend to snap on corners pretty quickly).
I got my SMMC4 yesterday, adjusted everything, and did a test run. Bought the 180 gram Special Edition pressing of Dire Straits' "Brothers in Arms" record just for the occasion, and it never sounded so good, in fact, I dare to say it sounds even better than the CD master.