Well, if people are really interested, I did it thusly:
1. I found one of these cables lying around left over from a portable DVD player I don't use anymore
To verify that your cable matches mine, measure the length of the 1/8" 4pin jack against a regular 3-pin headphone's jack and make sure they are the same length. Next, check the electrical circuit with a meter. From the wire-side of the jack it goes Ground, White-tip, Red-tip, Yellow-tip. If your order is different that is fine, all that matters is that Ground is the first pin. If not, then your wiring will be different.
2. Plugged this 1/8" 4pin headphone/composite cable into the long audio adapter which came with my TP
3. I found this splitter/adapter which came with my Mogul and broke it open with a knife
Inside you will see the wires from the TP spreading out and soldered to a breadboard. Each wire/contact is numbered in white on the breadboard and by cutting three wires and re-soldering two, the signals are re-routed to where they need to be.
stock arrangement:
6: Mic, Video Out
7: AudioR
8: Video Sense
9: Headset Sense
10: AGround
11: AudioL
Where I need them:
6: -> 10: Mic, Video Out
7: -> 7: AudioR
8: -> 6: Video Sense
9: -> NC: Headset Sense
10: -> 6: AGround
11: -> 11: AudioL
The wire running to contact 6 needs to be cut and reattached to contact 10.
The wire running to contact 10 needs to be cut and reattached to contact 6.
The wire running to contact 9 needs to be cut and isolated (open circuit).
The wire running to contact 8 needs to run to any ground, so I cut it and reattached to contact 6.
Now I put it back in the plastic case I broke it out of, taped it tightly shut and plug it into the completed cable. The adapter from step 2 above plugs into the newly arranged headset jack and a power adapter can plug into the left alone side with the power jack.
It needs to be said that the order on the RCA end is incorrect. The Red jack is AudioR, the Yellow jack is AudioL, and the White jack is Video. By cutting and resoldering one extra wire this could have been fixed, but I did not bother.