Actually, it's just as well that you don't have access to your TC-K700ES at the moment—I'm not enthused about taking this thing apart again today. So send along the picture when you have a moment, and I'll probably work on it again tomorrow or on Tuesday if I have time.
FWIW, I bent the arm just enough to reliably catch at the edge of the head carriage plate. Any less and it would not catch but scrape the carriage plate and engage the capstan. I can't see how the position of the arm would prevent the carriage from moving. Should it be possible to move the carriage manually?
Also, looking at the head carriage from the bottom in same plane as the plate itself, the left side of the plate is slight raised from the chassis, while the right side is flush with the chassis. Short of a complete disassembly and bending of the plate, I can't see how to level it on the left side.
In any event, when placing the transport in the PLAY mode, the plate doesn't move. Should it?