Both of those options were going to be next although I got the impression that telephone support didn't cover the advanced settings (was still going to try though).
Anyway, in the mean-time I've cracked it.
The solution was to switch off the machine completely (rather than using ipconfig /release /renew like I was) before adding the reservation in (from a different machine).
I now have static IPs on both Windows and Mint for the machine I wanted them for.
As always, thanks everyone for your suggestions.