Not sure if it helps, but I recently had exactly the same issue with exactly the same symptoms. Was worried it might be the logic board, but took my MacPro to a friends house to swap PSUs and check (he has the same MP). Installed his PSU and issue went away. With my PSU he had the same problem.
Ordered replacement PSU on AliExpress for $130.
Greetings,
Link to your order please. Thanks