With all these 'or' in between and jumping between various points, requirements and conclusions, it's a bit unclear what your're looking for.
If this is about most colour with least memory, then the (unofficial) modes Mode 8 and Mode 13 are your thing.
Or was it a limitation of bandwidth with the 6845 chip that couldn't handle both 320 horizontal pixels and 4bpp?
Short answer no. 320 pixel with 4 bits each equals to 1280 bit or 160 bytes per line. Double the maximum the Beeb design can do.
Yes and No. The 6845 doesn't handle any content or colours. It was originally designed to support a character based screen. It's just a bunch of counters to create sync signals and addresses during a frame. The 6845 only generates the frame. All content generation is external. The addresses were meant to access a linear character screen memory which then gets translated via a character ROM into rows of a character to be shifted into the video signal.
In the BBC the content generation is handled by a custom gate array (usually called Video-ULA) that takes the byte addressed by the 6845 and interprets it according to what's set in its control register.
While the 6845 can be put to use with a large variety of screen formats, it always comes down to the amount of bytes read in a line (*1). In the BBC it can be used to read 10, 20, 40 or 80 bytes per line. That's a maximum of 640 (80x8) bits per line. Resolution and colour depth are factors to this number, so quite simple:
Bits-per-Line divided by Colour-Depth equals Pixels-per-Line
Bits Colour Pixels
per Line Depth per Line
640 1 640
640 2 320
640 4 160
These are the absolute maximum resolutions per line at a given color depth.
And while there is no secret trick possible to read more lines, we always can read less per line and fewer lines. And that's what accounts for the memory 'saving' mentioned. As mentioned before, the system can be set to read less bytes per line, like only 40, which of course reduced the amount of bits read per line and thus memory needed - but also resolution as well. 40 bytes read mean 320 bits, which can be converted into 80 pixels in 16 colour mode and so on. The formula stays the same. Down to 10 byte per line mode giving twenty 16 colour pixels per line. Handy for some Pong or Breakout, isn't it?
Similar, lines could be skipped saving again memory.
Conclusion: Whatever resolution you want, you're restricted to a maximum of 640 bits per line to hold the data to be displayed.
Having said that, it may be possible to squeeze out a bit more by reprogramming the 6845 directly. Except, neither the OS nor BASIC will give you any support doing this - not to mention that it's not much and rather tricky to make it work within the timing of the Beeb's hardware.
*1 - Or more correct addresses prepared for a memory access.