The more I get to know USB-C, the more I like it.
It turns out that I believe both iterations of this project can be successfully powered from USB-C power sources.
The OCXO variant is fairly straightforward. Since it doesn't demand more than 1A @ 5V, there's no need to hook anything up to any of the pins other than the standard CCx pull-down resistors.
The FEI variant is a bit more complex. USB C can supply up to 100W, but negotiating the high voltage power that we would want requires some work. Fortunately, there are some very good solutions available. The best I've found is the Cypress Semi CYPD3177. That chip is a power sink negotiator, but what makes it particularly good for us is that it's desired voltage and current are set with voltage dividers, so there's nothing to program or set up. There's a "fault" LED that gets added that will light up red if the supply is incapable of negotiating the desired power (15 volts, 2.25A). Otherwise, the chip will pull down on a P MOSFET gate to send power to the circuit, once it's properly negotiated.