Can be more clear about these terms?
My knowledge make me think like that:
Muxed -there is some switch (ofcourse electronic one) that switch LVDS lines from integrated video to (discrete?) external video.
Muxless - is something like only one GPU is connected to LVDS lines,data is passed to other GPU then resulting video signal received and routed to outputs.
My oppinion is that muxless design isn't any good than muxed one.Just to make things easy and cheap.
In this case (SP55430) I think board ID is 01439 same like one of my notebook.
This board use muxed design.I know because I have modded mine.Lucky enough to find similar mux switch (in fact was some switcher from motherboard LAN port to docking connector,but same package,almost same pinout).And most important,board was designated for this,data lines was all connected,just second mux ic,few resistors maybe and few wires in LVDS cable between board and LCD display. Imagine that cost may be under 1$,real big increase in manufacturing cost
But that limit variant available or user choice to upgrade to FHD LCD display.
Now related to problem.
Code in BIOS exists but may be incomplete.
Real switching of graphics card works in certain condition. (under windows,using original drivers,at startup time if you power on notebook only on battery)
Resposable for switching is EC (embedeed controller)
Maybe under OS switching is done via DSDT,then we must find what is happening then simulate this in BIOS.
-When I say LVDS lines I was wrong a little,not only LVDS but all other signals,VGA,DVI etc.
-But once value saved,at some location in CMOS if BIOS ignore it and start in hybrid mode make no sense.
Find other free address where save this setting,test it few times to be sure saving-reading works.At this moment will be only nothing,same hybrid mode in fact but in BIOS you'll see integrated hybrid deficated based on previous choice.
If this happens then maybe BIOS itself at initialization rewrite this offset to be sure is in hybrid mode.