In answering this question, I found that there were multiple generations of 11/780 memory board, and so sizes, capacity, etc., are quite hard to pin down. I still have not found a board larger than 4MB.
I did get an answer for physical board size, though not for slot width (board separation).
One MS780 memory controller can take 16 memory array boards. For the original release of the 11/780, the boards were the M8210 or M8211 (32Kbyte/8Kbyte capacity, respectively), leading to a maximum of 512 KB per controller.
The system supported up to 4 controllers, thus a max of 2MB.
So, for the 'get a feel' part, that's up to 64 memory boards. If we assume the boards are spaced at least 1" apart (I could not find slot-size info), that's over 5 feet of memory alone.
ECC was used, 8 check bits per 64 data bits.
The board size us 12.5 x 15.5 x 0.75 in; I assume the 'depth' includes the tallest chips.
The board numbers came from the MS780 memory system tech manual, see figure 1-1 on page 1-3.
Here's a link to an M8211 catalog entry in the Computer History Museum. When they say '64K module' they apparently mean 'bits'.
Later memory boards increased the board capacity and thus the system capacity. My 1980 "VAX Hardware Handbook" (includes the 780 and 750) has the following:
- Per chip 16K bits
- Per board 256KB
- Per controller 4MB
- Per system 16MB
The physical board size won't have changed for these though.
This 1984 print set for the MS780H memory controller talks about 256Kbit MOS devices, which squares with the OP's chip identification.
The memory board appears to be an M8374, a 4MB board (which nets out to 144 chips including 1 check bit per byte; the print set say there are 156 RAM chips).
The system might only support 2 controllers at this point though. It's not clear to me what is authoritative.