The HP5315A/B & HP5316A/B Reciprocal Counters were manufactured with a variety of 10Mhz time bases, including onboard and modular basic oscillators (XO), temperature compensated oscillators (TCXO), and for some series numbers, an oven controlled oscillator (OCXO).
For the very best stability and performance an OCXO is desirable but originally very expensive. Now it is quite cost effective to up-grade one of these meters with our OCXO kit! We are offering two kits at this time. Each kit contains all of the required components including mounting hardware. One kit includes the Morion MV85 10Mhz oven module, while you supply the oven oscillator in the other kit. These OCXOs are readily available at such markets as eBay and Aliexpress.
The kits are all through-hole mounted components, so only modest soldering skills are required. Thanks to AMC184 on EEV-Blog for the original PCB artwork of which this is a derivative! Our kits use quality low ESR capacitors for the best stability and 1.5A LD1086 or 3A LD1085 low dropout regulators to power the OCXO module.

You should be able to set the counter timebase to 10Mhz +-0.1Hz using a GPSDO directly to get 10.0000000Mhz in the display. You can likely get even better using differential phase timing with a stable oscilloscope or using other techniques.