You’ve covered all the bases on the wiring checks.
Reading 429 data bus wires requires an adapter.
The RTX adapter was the cheapest I could find. It is a single channel “receive” only. Numerous manufacturers have their own software and adapters.
These usually have multiple transmit and receive channels. They’re not cheap. My RTX was about $800US.
I would see if one of the user units has a bad 429 receiver (which I've seen before) which is locking up the entire data bus.
Disconnect one to see if the other two come up. If not, hook the first one back up and try another. Try it again on the last unit.
Is either of those data bus wires shorted to shield or ground??
Do any displays show annunciation or range marks that would indicate the data "is" reaching the display, but not the actual weather? If that was the case then you would need to go back upstream to the antenna input.
It looks like you've got a jumper that tells the unit to send the output to EFIS, is that present?
If things are working fine for 10 minutes and then not..... it sure sounds like a component is heating up and then failing. I'b bet it is the indicator.
Is Nav Tuning from the Garmins or is there separate Nav Control Units?
If the Garmins are tuning, it looks like those tuning requests go to the DME Master Indicator (KDI-574) on pins 11, 12 and the J-Box on 70, 51. from there the J-Box feeds the request to the DME (KN-63) on pins F, 6. The DME output goes back to the J-Box which feeds the Arinc Adapter (KDA-689) which outputs 429 data back to the GNS (I only see an output to the left unit).
If I'm correct, this still leads back to a tuning issue from the #2 (or right) GNS. I circled some wires to check on a previous post. The "RNAV REQUEST" signal from each Garmin looks to be the signal which tells the Master Indicator which side (GNS request) to forward to the DME.
If those four wires (18, 19, 20, 22) check good from the #2 GNS..... the Master Indicator would be the most suspect unit.
Also, three of those wires are connected to each other via splices. To make sure one Garmin isn't loading them down, try each alone with the other GNS not in the system. In your case.... disconnect the #1 GNS to see if the #2 tunes and displays properly.