How can I configure a headless MacMini controlled via Remote Desktop to match the remote resolution ?
Unfortunately, when no monitor is attached, macOS uses a hardcoded list of available resolutions, and you cannot change this resolution by the mechanism that SwitchResX uses. Thus you cannot modify this to match the Remote Controller's native resolution.
The only way would be to make the Mini think there is a monitor attached (using a dummy video adapter that simulates a monitor) - this one can then be enhanced with SwitchResX to match your requirements.
Example if your mini has a MiniDP port, then you can use an adapter like any MiniDP+USB to HDMI adapter:
This kind of adapter includes some electronics and fools the Mac into thinking it has a real monitor attached, and then uses the signal to recreate a HDMI signal (including sound, but in your case you probably don't care). When this adapter is plugged, the Mac doesn't see your monitor directly any more, it sees the adapter, and enables resolutions up to 1920x1080. Then, maybe SwitchResX can enhance it to 2560x1600, even if I'm not 100% sure for all kinds of adapters.
Don't just use a pass-thru adapter, without electronics, which would require a monitor to be present.
When it's a pass-thru, you still see the original Monitor name in macOS.