SuperSleeper, I got my car back for now. Since you were interested I'll tell you what I learned.
The mechanic that worked on it wasn't available, but I did get the broken sensor back. I then took it to the local auto parts shop to see what I could find out.
So here's the broken sensor (view from the underside):
I just marked the points of interest with arrows.
The guy at the parts store said he sells these all the time. From what he's seen, the failure is usually where the green arrow is. That's the rubber seal that mates with the rim. It made sense how over time the seal can wear out. However my sensor has a bigger problem: the stem is broken.
The broken stem (the red arrow) wasn't something he'd seen before. On the way home I stopped off at a different local garage to try and get a quote (more on that later). The shop owner there told me that the stems on these sensors are made of aluminum and in his experience they become brittle and are prone to breakage. He called it a "bad design." No kidding. Though I'm sure it's a great design as far as sales are concerned.
When I got home and took the sensor out of the bag it was in, I discovered that the rest of the stem wasn't missing. It's embedded inside the stem cap! Apparently at some point the tip of the stem seized inside the metal cap. Not sure why... the cap is stainless steel. Anyway, when the shop tried to remove the cap, I bet the stem snapped off. Lesson here: if you have TPM sensors, don't use metal stem caps.
It just so happens that my other 3 stems all have plastic caps, thankfully.
What did I learn about pricing?
Shop #1 quoted me $130 which I think included mounting & balancing, but I need to double-check. I'm waiting to hear back about whether or not they will let me supply my own part.
Shop #2 quoted me $130 for the part and $150 installed. Their policy is that I cannot supply my own.
Shop #3 said that they would need to order it from the dealership and wasn't sure of the price. Their mount & balance fee was $15. This garage is willing to let me buy my own sensor.
I checked 2 dealerships (from their online parts catalogs) and the dealer prices were about $75 and $90 respectively.
The auto parts place has several of these that claim to fit my car ranging from $45 to about $110. The guy did a cross-reference of the part number from my actual sensor and found one unit that was a direct replacement for $65.
I can get one online for $35+shipping, and most of them seem to be between $40 and $70. However, I'm not sure what the differences are. It's probably worth going with the one from the auto parts store that came up as a match.
So that's what you can expect to look forward to if your next car has these things.