Hi Julian,
I have used an SME 3009S2 improved on my 370 and although it did sound nice switching to a Mission 774 made a big difference. There is a definite synergy between the 370 and 774, I would definitely recommend it.
I think most 370 plinths were cast for the SME type mounting but there are some with the Rega pattern, perhaps that is why the OP was experimenting with other arms with that mount.
Walpergis ( Geoff ) is the man to ask as he knows these decks very well.
Turntable
Toshiba SR-370/Mission 774/Van Damme cable with MS Starline plugs/Ortofon Quintet Black
CD
Cambridge CXC transport/modified Musical Fidelity X-DAC/modified Musical Fidelity X-10 V3 tube buffer
Network Player
Cambridge NP30
Amplifier
Denon HA-500 head amp/Nakamichi CA-5E pre-amp/Chinese passive RVC/Proton AA-1150 DMC power amp
Speakers
Mordaunt Short Signifer on original factory stands
Cables
Mogami with Rean Neutrik plugs/NVA LS5
Headphones
Sennheiser HD600/Sennheiser HD650/Koss Pro4 AA