OK, thanks guys, success!
Didn't change the configuration, but rather how the new Airport Express was how introduced. What remains the same: Internet provider ethernet to Airport Extreme wireless base station; wireless to new Airport Express; ethernet from new AE to Transporter; computer with Squeezebox server wireless to network set up by Airport Extreme and Airport Express.
What's different and now working: I now set it up as a WDS, but luckily using the much easier path because both devices are wireless N. From the perspective of the Mac/Airport network, this is manifested in changing how the Airport Express was introduced. At first it was "join wireless network". This didn't work. The new approach was to go first to the Airport Extreme base station and check "make network extendable". Once that was done, I went to the Airport Express and selected wireless mode was "extend wireless network", rather than "join network" as before. That's it.
The first indication this worked was that when the TP was still operating wirelessly, the signal strength jumped from the 70's to 100%. So it was clear that the network was "extended" and it got it's signal from the new Airport Express plugged in right behind it. Then I plugged in the ethernet from new AE to TP, had to reboot the computer, and set up the TP as an ethernet network. No problems. Everything works. Also, I checked "info" on the settings window, and there is no longer an indication of "wireless signal strength", just to reconfirm that it is using ethernet. Also, now I'm able to take off the antennae.
Thanks everyone!