Front should work in friction mode. No problem. It will actually save you lots of pain related to adjusting it.
As people said, the rear will not work.
- SL-BS64 Shimano (probably discontinued, you still may be able to source them somewhere) or 8s Microshift https://www.microshift.com/en/product/bs-a08-bs-t08/ should work with Shimano RD. You only need the right one if you can tolerate mismatched shifters.
- A more exotic solution: your shifters will allegedly work with an 8 speed cassette with a pre-1997 Dura-Ace RD: https://www.cyclinguk.org/cyclists-l...imergo#Shimano This is not ideal, and it will probably lack the needed chain wrap capacity (Dura-Ace is "road", it has shorter cage).
- As people said, get a 9 speed chain and cassette. Your M310 RD may or may not work well.
- Or run 8s in friction mode.
- Or employ some other solution people suggested.
Having said that, why not give Suntour RD a shot? It may have a different cable pull ratio, and who knows if it coincides with old Dura-Ace?
