"Limited to a 10 s gate, the 5386A is really not much more accurate than ~0.1 Hz. "
that not true , this type of counters are second generation, able to measure phase shift between signals, with minimal jitter and 10M source usually are, it perfectly measure extended 11 digits. in practice im able to compare with 100 and 1000 sec period with other counters, with the same result.
CETC institute has a lot of documents in PDF publicity available but i think around 2016 access to the web site was blocked. as it basically close to military. i may mistake but as far as remember OSC5A - AT cut , OC5SC - SC cut, with better long therm.
12volt OC12SC36 - has better volt sensing circuit, in my practice approx 0.3mV to adjust greater accuracy. and that as well force to use very well stable source of adjusted voltage. the best result i got when voltage source thermally connected to OCXO case, basically thermally stable, with some additional thermal isolation i had drift in -2-10 \Y (really no. remember, but perfectly fine for 8d direct counter) as well it help in 1-decrease power consumption. 2-much better temperature control. 3-decrase jitter due to temperature deviation.
"cheap little pot" - use the same, not affecting at all, in a correct circuit adjustment has to be a small fraction of total regulated voltage, so ideal rough adjustment inside the heated chamber, and superfine outside.