If anyone is interested in enabling their counter, I have 4 extra LMX5080 after over a month waiting for them to ship.
$5 each, shipped from USA.
Many thanks, the chips arrived a couple of days ago, but I'd forgotten to order an appropriate RA BNC. That arrived this morning, and the HF counter now works!
The HF counter seems a lot more sensitive than the LF one.
In addition, the internal reference is a whopping 42ppm out.
The pic was taken with a common rubidium source shared between the RF signal generator and the Hantek. There is also a bit of uncertainty depending on when the gating happens in relation to the input frequency, more than I'd expect. The gate time also seems a lot longer than what's programmed in.
Edit: Regarding the RA BNC, the one I purchased had ground lugs too big for the PCB. I tried filing them down but the metal was very soft and the lugs snapped off, so I filed them down, tinned the ground pads and the connector and treated it as an SMD part, reflowing it with a hot air iron and copious kapton tape around the area to stop the other parts from running off.