Medici are undervalued. The brand history does not help. I have one also, earlier model before they added shooting stars to the downtube graphics.
Different lugs too.
If the rear derailleur indexes reliably with that rear mechanism, freewheel and shift levers, terrific. And Exceptional luck.
I think you may have to go to friction mode or get a full system designed for each other. I am not sure where to place the anchor point to build from.
Suntour hubs... if early enough to use a freewheel, then possibly build into a 6 speed DuraAce freewheel, derailleur and use those shifters, Which I think are 6 speed when SIS launched. DuraAce used a different cable pull ratio than other brands.. If, freehub... I would probably go retro-friction, or plain friction shift levers.
Cranks are nice, brakes have a following, but are esoteric.
You know what you need to do for the stem and handlebars.
Alternatively, sell off most of the parts, find a donor bike with Shimano 600 tricolor, have a fat wallet and be happy. Leave the Super Record headset.