How to get 4K Resolution on a Headless Mac Studio (M4)

I just picked up the new Mac Studio (with M4 Pro chip) and have been struggling to run it effectively as a remote headless system, using my iMac as a monitor.

Basically, I am ONLY able to connect to it at HD resolution using Screen Sharing from my iMac unless I have an active external monitor also connected. So if it's connected to a 4K TV over HDMI then I can access it at 4K, but if I turn off the TV or disconnect the HDMI connector then it is back to a single resolution option: HD.

Reading older conversations on numerous forums it seems the classic way to work around this limit is to use a dummy plug that spoofs the system into thinking that it has a higher resolution monitor attached... but despite having tried out four different versions of dummy plugs that claim 4K support (1 Thunderbolt, 2 HDMI, 1 DisplayPort with adapter), each of them still max out at HD resolution.

Now, they are doing something when connected: I see LOWER resolution options when any are attached (instead of a solitary 1920x1280 display option if nothing is connected). But they never trigger anything greater than HD to show up in my display settings.

Has anyone had better success using dummy plugs, or any other method than just connecting a 4K monitor?

Oh I will note that I was able to try it with a Vision Pro... and that will happily give me 4K, double-wide, and ultra-wide resolutions as long as I'm connected to that. So it should have been possible if Apple wasn't blocking it from working?

Tested with the latest Sequoia 15.4 update today.