I experience exactly the same issue as you, only with XFX 5700 XT model.
I never had any signal through HDMI port, will try your "split second" solution with second monitor and will let you know the results. I do not use HDMI at all, so If I find that my HDMI is not hardware faulty but only has problems like yours, maybe it will relax my OCD feeling and I wont RMA card.
Also one more question, will it work if you try only 1 monitor on HDMI? And did it work in the beginning without problems on hdmi?
Thank you, update soon to come
A Make-Shift Fix is to create a Custom Resolution / Timings for the HDMI Display.
I recently had this issue with my RX 5700 XT., as I'd been having an issue that whenever the Display (Smart TV) went into Screensaver Mode; it would result in a loss of image on the TV.
Now as a note, the Drivers / Windows would still CLAIM they were outputting fine; and even the Smart TV would report that HDMI was connected and working fine but obviously a black screen as no image was actually being output / received.
Ultimately what I ended up doing was resetting the Smart TV to Factory Default., this reset the Timing Tables and the image returned... but there was another Monitor TV that I had, which also had said issue that I couldn't do that for as it had no option.
What I had to do for that was create a Custom Resolution (Manual Timings) and this resolved the issue there.
What I find most interesting, is even switching to a DP-to-HDMI Converter (Active in my case., as my Display is UHD 4K) the problem persists. In essence what seems to be happening is a Sleep Signal seems to get stuck "On" for a given display.
I'd say this is a Driver issue, but as it persists even during Boot... well it makes me think that something is happening with the Display Timings Table; like Metadata is getting stuck "On", but as I said a Custom Resolution / Timing will resolve it; and I'm certain it's because it Omits / Resets all Metadata.
Got the same thing. I created a custom resolution. Still no HDMI signal but (HDMI is active because devices handshake) so I deleted the custom resolution. THEN suddenly there was a full HDMI signal. Looks like this has to be reported as a bug to AMD if it has not been already.