"...Is this how long the wire runs between the transmitter and box?"
The "wire" seen in the photo runs from the antenna to the antennna controller (in the man's hands in Randy's pictures at the top of this thread). The Receiver, not the transmitter, connected to the controller, and through it to the antenna. The loop antenna was only used for receiving. The controller was mounted on the instrument panel, where it stuck out in a convenient place for Amelia to operate it (I'll try to find the photo). The controller rotated the antenna and indicated what direction the antenna was pointing. It also allowed the number of turns of wire inside the antenna to be selected for best frequency sensitivity.
Correction - a normally reliable source tells me that the controller only provided tuning of the coil, using capacitors, and such. Rotation was by other means, possibly a handle sticking out from the antenna through the cabin roof.
Nice clear view of Amelia's shoe.