With great help by user Michael Karcher we found the following details poking through the V6366 controller's innards:
102 (outside of V6366, the decoded I/O select line is called VDCS)
00: Plasma panel active
20: External monitor active
CRTC index port
CRTC data port (6845 compatible, except for "interlace & skew" ...
Another partial answer:
Contrary to my first impression (by analyzing just the INT 10 handler it provides), the BIOS does in fact contain code that interfaces with the extended registers of the V6366 video controller. But first let's take a look at the schematics at page 22/23:
Obviously, the only video RAM chip is the 32Kx8 SRAM U6, so the V6366 is ...
I was unable to find [the low level programming] documentation.
Perhaps they can give a clue as to what ports to look for.
The datasheet you linked says the V6366 is compatible to the MC6845 except interlacing and skew, and also compatible to CGA, MDA and Hercules.
That already gives a good idea what the registers look like (...