Colin I think I know why you loose GPS after plugging in the 3rd flvss.
Triggered by your issue I did some research on a way to improve the current packet scheduler, you can find my article here
Back to your problem, you have 4 external sensors plugged on the bus in addition to ardupilot acting as “virtual” sensor 0x1B, by looking at this table
you can see that your telemetry stream is at 14Hz, so ardupilot gets a chance to send a telemetry packet every 72ms.
The default ardupilot packet scheduler is unable to cope with such a low telemetry data rate and lets low priority packets (gps in your case) starve.
In the current scheduler GPS is the packet with the longest period (1000ms) so it never gets a chance to be sent.
Would you be interested in trying an alternative scheduler to see if it fixes your issue?
What plane version are you using?