@ viper z
I have very good results with narrow 9-speed chains on 7-speed freewheels.
On my bad weather bike I have run Rohloff 8-speed (7.1 mm wide) and 9-speed (6.8 mm wide) chains with Sachs 7-speed and Regina Syncro 7-speed freewheels. They work very well together with a C-Record rear derailleur and C-Record crankset. With this setup, I tested the Syncro II levers with the blue insert and shifting was fine with overshifting the levers towards larger cogs.
I returned to friction levers because I now use the Syncro II levers with green insert together with an old 1987 Chorus rear derailleur (the one with the adjustable parallelogram, probably Campy's first slant parallelogram derailleur?).
Together with a ShimaNO Hyperglide 7-speed freewheel (14-28 T) and a Rohloff 9-speed chain, Syncro II index shifting is flawless! What a modern freewheel and chain can do.
Best regards from Germany