I ended up hacking the radio firmware to bypass the signal processing and stream the raw received samples from London to Sydney. I hacked a radio in Sydney to feed the London samples into its signal processing, then streamed the resulting samples back to the transmitter in London. I now had an LMR base station running in real-time over the Internet, with the radio hardware in London and the signal processing in Sydney. I was able to attach a JTAG hardware debugger to the DSP in the radio running the signal processing and find the bug. From there we did a firmware release and uploaded new firmware into the radios in London. Our radios stayed in and handled the stage management for the Opening Ceremony of the London Olympics.
Edit:
The customer must have been happy with the outcome, as they ended up using our radios for the Sochi Winter Olympics two years later.