Finally scored a ABS/TRC/VSC module (P/N 89540-35270) on eBay for a decent price ($119 shipped). It was from a rollover and had some surface rust, see below. For anybody looking for these, on junkyard search engines they are listed as "Computer Box Not Engine" and go for around $200-300. On eBay the Buy It Now listings are usually $240-300.
Bolted it in and hooked up all the harnessing, and all the lights went off except Check Engine, VSC OFF, and VSC TRAC. Drove it around the block to confirm that the speedometer and odometer were working again. I then used my OBDLink MX and my phone to clear the codes, and all the lights were off. I was a little surprised that the VSC lights went off because I thought I might have to recalibrate the vehicle yaw sensor with this new module, but apparently not.
Anyway, figured I'd update this with the resolution for anybody who has this issue in the future. I might tear open the old module later to see if I can figure out what went bad with it.