The VT268 programming guide (mirrored
here) does explain some of these mysteries. I'm not sure about the VT368, as it's not publicly documented, but it can probably be assumed to be an enhanced VT268.
The VT268 does have some high resolution output support, supporting a 512x240 sprite layer AFAICS. This is done with minimal hardware tweaks by having two render paths for each half of the screen. Maybe the VT368 has even more support for high resolution output. Even on the VT268 it might be possible to exploit interlacing to get up to 512x480, maybe that's done badly for some reason explaining the B&W output.
In theory the VT268 only supports 128MBit (16MB) of ROM. This may be higher again on the VT368, or larger ROMs could be connected to the VT368 using GPIO to bank switch the upper address bits. Alternatively some systems use the "fake cartridge" method to switch between ROM banks.
The addressing system of the VT268 is also interesting because instead of the complicated address translation in the VT168, the 6502 CPU has been modified to allow 24-bit addressing directly from the CPU. This unfortunately is documented in a separate document that is not available, however I think it can be reverse engineered easily enough as EmuVT will disassemble all of the new instructions - and I believe it may be similar, at least to some extent, to the 65C816. For use in multicarts and for backwards compatibility with older 6502 code, the VT268 does also support applying a fixed offset to the address.
There are definitely VT268 systems in circulation as Cube Technology claim to have developed games for it.
Hopefully I'll be able to add this to my emulator once the VT168 stuff is working well enough. Then maybe it will be possible to reverse engineer the changes in the VT368 assuming it's not too different from the VT268 (or VT168).