I finally got time to break out the multimeter. I found two things. 1) 3 of the 5v+ pins were actually dead (not properly connected) and 2) I was hooking the thermistor to the wrong pin (I have two temp sensors but only plug in one for testing).
In addition, powering things in a chain as diagrammed above is perfectly acceptable and works. I tested the various sensors at various loads and the pins downstream and upstream still read 5V+ as they should.
So, what can we learn from this... When in doubt break out the multimeter and take good notes. Also, you can use a deprecated IC socket + male header pins for a quick plug and play power hookup, but its probably not a good idea for a finished project.