The NixiSat is definitely a BNC connector. The problem with replacing the BNC in the NixiSat enclosure is Jeff glued these to the wood. Trying to remove would most likely damage the finish or possibly destroy the wood. I'm sure you may be able to apply a heat gun to it, but you still run the risk of damaging the finish.
This is why I wanted to retain the BNC if possible. Unfortunately, the BNC is a two conductor.
So your NixiSat very likely needs just three wires... +5VDC, GND and GPS TXD... Checked my assumptions and it turns out the GPSII doesn't need the 1pps signal. Works fine with just a GPS NMEA stream. Your NixiSat may well be the same.
Given just three wires, how about bringing TXD and GND in on the existing BNC and finding a way to add a +5 wire somewhere else on the clock? Might be possible to inconspicuously fit a well insulated wire between the bottom of the wood and the base?
I'd bet NMEA is supported... At least a few Oncore models could be configured for NMEA output and the NixiSat description references NMEA in the command list. Certainly the same or very close code base as the GPSII:
8) Coordinate Scrolling: 0 = disabled, 1 = enabled. You location coordinates are scrolled in degrees, decimal minutes and decimal seconds, in accordance with the NMEA-0183 specification.