In retrospect, the "right" (but slow) way to go would have been to order the parts I need instead of just hacking something together with the parts I already had.
In particular, it would be a lot easier to just order a known-working 1.8v USB serial adapter instead of attaching resistors and diodes to a 3.3v USB adapter to shift the logic voltage levels. In addition to shifting logic levels, the USB adapter also had to be modified to allow the kindle TxD output to pull the adapter RxD input down to a logic zero (by removing an LED).
Also, it would be much more "professional" to use the right connector instead of soldering wires to the serial port pins inside the kindle.
But a quick hack often gets the job done much faster than waiting for the "right" parts to arrive (especially cheap parts from China).
The serial cable has now been unsoldered from my kindle touch, and the back cover is installed. Now I can hopefully leave the back cover on it for awhile.