Well... just after I posted this, I had a feret around through one of the Older Software mirrors and came across the G3 Ethernet update 2.0.4, containing an update of the Apple Built-In Ethernet extension that was intended to fix seemingly the exact issue i was having, with it being perculiar specifically to the beige G3, as best I can tell.

The 9600 now mounts the drive over the network from the G3, and the G3 seeing the 9600.

So for future reference, if you have this issue, grab yourself a copy of the G3 Ethernet 2.0.4 update and replace the existing built-in ethernet extension with the one included in that update package.