I don't have TWRP installed on my Nexus 7, instead just using fastboot to boot it when I need it for something, so the technique that finally got the binary updated was to tell SuperSU to use the TWRP update mode, then when it I got the popup saying it was about to reboot to recovery, I plugged in the USB cable and ran:
adb reboot bootloader
fastboot boot openrecovery-twrp-22.214.171.124-flo.img
That worked. As soon as TWRP booted, it installed the script SuperSU had prepared for it, and the binary was indeed updated.
I never had a problem with the "normal" binary update method before. Something new and "helpful" in 4.4.3 I guess.