Maybe an EDID emulator can solve the problem. I'll explain later if you want, busy now.
I mention in passing that the HD Fury Dr. HDMI 4K did NOT work for me, in successfully facilitating one of my cabling approaches which involved using BOTH the HDMI1-out and HDMI2-out of my Yamaha RX-A1080 AVR. This was the theoretical alternative to using a single splitter on HDMI1-out which actually DID work to feed both TV (in 4K) and A16 (in 1080p) from the single HDMI output of the AVR, using the two outputs of the AVR instead.
Although the splitter method did accomplish the goal, it was at the expense of losing eARC and also HDMI-CEC, and in the end I decided that was to great a cost.
So using the two outputs of the AVR itself, as if it were the splitter, was the next idea. The original failure with that was that both supposed TV's (connected to the two HDMI outputs of the AVR) had to be 4K, in order for sources to send 4K. With only the A16 connected to HDMI2-out it appeared to be only 1080p-capable, so I only got 1080p on the primary HDMI1-out going to my real LG C9.
That was when the Dr. HDMI 4K EDID emulator was proposed as a possible solution, and I bought one. With no instructions provided but the item having both HDMI-input and HDMI-output, it wasn't obvious to me whether I should cable AVR -> Fury -> A16, or AVR -> A16 -> Fury. I decided it was probably the former, so that the Dr. HDMI 4K could represent a 4K TV supporting both Dolby Vision and Dolby Atmos (presumably what "FS", i.e. "full sound", was intended to imply). Again, it would have been helpful if instructions had accompanied the product.
Anyway, I was simply unable to get it to facilitate dual-output from the AVR. I tried the Fury set at "green-1", which is maximum 4K 60fps video and full-sound audio, cabled between AVR and A16. But for some reason there was then no video output on HDMI1-out of the AVR going to the TV. Then I tried dropping the Fury down to "green-3", which I think was annotated on the unit as "DV1 for LG C7 with FS" (which I took to mean Dolby Vision for the C7, but I don't see why green-1 didn't work). The green-3 setting didn't work either.
In the end I just removed it, as an unsuccessful experiment. The objective would have been to support almost all configurations and situations without requiring a physical move of the HDMI cable going to the TV, from HDMI-out on the AVR over to the HDMI-out on the A16 (which has to be done in ANY setup no matter what, in order to get eARC audio to the A16 and headphones). As it turns out, reverting back to my very original cabling setup accomplishes exactly the same thing, without a splitter and without the Fury and HDMI1+2. Yes, I still have to move the TV cable to the A16 for eARC audio from headphones, but leaving it on the AVR supports eARC audio from speakers. And leaving it on the AVR supports all other sources coming through the A16 (just that it must be powered on).
I'll be glad to sell my Dr. HDMI 4K at 50% off to anyone who wants to try it. It did arrive quite promptly from China, at $119 + $28 shipping = $147. It's yours for $75 from me with free shipping.
So, to summarize my cabling:
(1) A16: HDMI-out -> video to HDMI3-in of A1080 AVR
(a) Oppo 203 HDMI2-out (audio-only) -> HDMI1-in of A16
(b) Roku Ultra 2020 -> HDMI2-in of A16
(c) ATV4K 2019 -> HDMI3-in of A16
(d) Shield Tube 2019 -> HDMI4-in of A16
(2) A1080 AVR: HDMI1-out video -> HDMI2-in of LG OLED C9 (automatically also facilitates eARC audio from TV apps back to AVR and 2.0 speakers)
(a) Oppo 103 HDMI1-out (audio/video) -> HDMI1-in of A1080 AVR, audio output -> downmixed 2ch-stereo for 2.0 speakers
(b) Oppo 203 HDMI1-out (video-only) -> HDMI2-in of A1080 AVR
(c) Oppo downmixed 2.0 stereo L/R analog output -> DBX 14/10 EQ (tone control) -> analog input associated with HDMI2-in of A1080 AVR, for 2.0 speakers
(d) A16 HDMI-out -> HDMI3-in of A1080 AVR, audio output -> downmixed 2ch-stereo for 2.0 speakers (requires enabling "HDMI pass-through" on A16)
(3) Oppo 203 HDMI1-out video -> HDMI2-in of A1080 AVR
(a) WMC Linksys DMA2100 extender (for cable/OTA HDTV) -> rear external HDMI input to 203, delivering 720p/1080i HDTV deinterlaced/upscaled 2160p to LG OLED C9
(b) downmixed 2.0 stereo L/R analog audio output -> DBX 14/10 EQ -> analog audio input for HDMI2-in of A1080 AVR
(4) For eARC audio from headphones, the AVR-end of the HDMI cable going to the TV is temporarily moved from HDMI1-out of the AVR over to HDMI-out of the A16. Also, a second HDMI cable is temporarily used to connect any HDMI input of the A16 to HDMI1-out of the AVR. Otherwise, for eARC audio from AVR and 2.0 speakers the normal cabling arrangement provides this automatically when a TV app is used as the source for audio/video.
(5) To listen to sound through A16/headphones the A16 must be powered on and the AVR can either be powered on or off (as "HDMI standby-through" is enabled on the AVR, input video is always output to the TV and this does not require the AVR to be powered on). To listen to sound through 2.0 speakers the AVR must be powered on. For HDTV sound from speakers the A16 is left powered off (since analog audio from the 203 goes through the 14/10 EQ and on to the AVR analog audio input).
(6) For 2.0 speaker sound from the three streaming sources going into the A16 (only theoretical, since I normally listen to streaming sources through A16/headphones) the "HDMI pass-through" feature of A16 must be temporarily enabled and the A16 left powered off. This will send multi-channel source audio along with source video from streaming source to HDMI-out of the A16, and into HDMI3-in of the AVR which is powered on. Sound is presented as downmixed 2.0 stereo via 2ch-Stereo on the AVR.
(7) The inherent conveniences of HDMI-CEC for all devices, facilitated primarily through the direct HDMI cable between HDMI1-out of the AVR and HDMI2-in of the TV are simply advantages you cannot live without. For example, to make use of my new Silicon Dust HDHR Flex 4K ATSC 3.0 OTA tuner (supporting both ATSC 1.0 and 3.0 broadcast channels) I use the HDHR app that runs on the LG TV. Pressing the Power button on the TV remote gets things started, powering on the TV and also the AVR. Then, using the TV remote to select the HDHR app on the LG automatically activates eARC to deliver 5.1 audio to the AVR. And this in turn automatically causes the AVR to switch to AUDIO1 on the A1080 (used to be AV4 on the A860), which is where eARC audio-only goes into the AVR for presentation out of its speakers (in this case, downmixed to 2ch-stereo by the AVR). All this happens automatically from just (1) powering on the TV, and (2) selecting the HDHR app on the TV.
Similarly, if I want to watch/listen to either Oppo 203 (for disc) or one of the three streaming sources going into the A16, I of course have to power on the A16 and wait for it to stablize. Then I pick the proper preset which relates to the A/V source I'm wanting to use. With these required preliminary steps done, I now just power on the particular source I'm wanting to use with its own remote. That automatically powers on the TV, and powers on the AVR, and automatically switches the AVR to select HDMI3-in (which is being fed by the A16, i.e. passing through any of the streaming sources feeding into the A16), as all sources into the A16 are seen as the one HDMI3-in to the AVR coming from HDMI-out of the A16. So with one power-on of the specific source to be used, the TV and AVR both power on and the AVR selects the appropriate input to pass-through video sent through the A16 on to the TV.
For watching HDTV (via the WMC extender fed into the external HDMI input of the Oppo 203 and on to HDMI2-in of the AVR) again it's just press the power button of the 203's remote (after turning on the WMC extender). This automatically powers on the TV and also the AVR, and also automatically switches the AVR to HDMI2-in which is the input coming from the 203. No need to power on the A16 since I'm just listening to 2.0 speakers for everyday HDTV usage. But it all happened automatically just from the single POWER press of the 203's remote.
The wonders of HDMI-CEC and HDMI inter-connects.
That's why in my opinion any cabling configuration that concedes HDMI-CEC or eARC (e.g. when the splitter is being used) is not an ideal one. These are just too great a pair of conveniences to be written off for some other minor advantages. They should both be base requirements of the setup.