Progress!
First revision boards are ordered now.
I found some other prescaler part number datasheets that mention the spurious count thing and suggest a 10K resistor to VCC from the unused channel for a couple mV of bias (and the resulting decrease in sensitivity).
So I have made a provision for a resistor and also a capacitor for good measure (extra pads to play with 'just in case').
Once the boards arrive, I'll try this and that and have a play around to see what happens.
I'll need to get a function gen that is good for a bit more than 3GHz (my gear currently tops out just a bit above 1GHz with a Tek SG504) so that's on the 'gear acquisition list' now too.
I think I should be able to use my 8481A/E4418B power meter to roughly characterise the input response at different bias voltages too.
Jared.