I think I've just worked out that all the single-char Japanese characters run on from the ASCII numbering sequentially in Cyber Knight.
For example, look back at the first font image - all the ascii chars are in sequence, and they are represented by standard ascii hex codes in the game rom. Fine so far (but a nice easy way to start!).
Now, look at the font tiles that come at the end of lowercase 'z', a gun, a sword, a right chevron and a red block, followed by the single Japanese characters. If you number these with the ASCII sequence immediately following that of z=0x7a, then you get the gun=0x7b, sword=0x7c and so on. The Japanese characters also continue that sequence sequentially, so 0x81=small_o_symbol, 0x82=left_upper_right_angle and so on.
I haven't gone all the way through the first page of fonts yet, but from those I've tested so far (the main title screen is the easiest way of doing this - simply replace the ASCII codes for CYBER KNIGHT with them and it works 100% so far (ie you get "CYBER <gun><sword><chevron><block>"). If everything is sequential it will make it a lot easier to construct the mapping table.
The image shows the result of changing the ASCII sequence for "CYBER KNIGHT" to the hex codes:
0D 06 7B 7C 7D 7E 81 82 83 84 85 86 87 88 00
Which begins after the end of lower-case 'z', and shows that the numbering of the font tiles is contiguous with the ASCII sequence at that point - what a stroke of luck!
EDIT: I have to say, every time I look at that dull menu screen I die a little bit inside. It's like they didn't even bother trying.