I was able to fix this and get 4.3 installed. Since I couldn't find a walkthrough for this, here's what I pieced together in case others have the same problem.
First, you need the right debuggerd file. For the 4.3 update (coming from 4.2.2), you can get a copy from this XDA thread (post #4 by tiggggr).
Now to get it in the right place. There are a few ways to do this. I used adb but it can probably be done with most file explorer apps. First copy the debuggerd.rename.zip you downloaded onto your device somewhere:
adb push debuggerd.rename.zip /sdcard/debuggerd-4.2.2
Then you need to be able to write to the system partition, stop the debuggerd, make a backup if you want, then copy the file:
adb shell
shell@android:/ $ su
shell@android:/ # busybox mount -o remount,rw -t auto /system
shell@android:/ # stop debuggerd
shell@android:/ # cp /system/bin/debuggerd /sdcard/debuggerd-backup-old-bad-version
shell@android:/ # cp /sdcard/debuggerd-4.2.2 /system/bin/debuggerd
shell@android:/ # sha1sum /system/bin/debuggerd*
a2323a0c8e245e3879d6b8beff6b2c4802045271 debuggerd
df2e705da097e4d535b4f4d98fab3bd76601e76c debuggerd.backup
I had to do a similar thing to restore my build.prop from a backup on my device:
root@android:/system # cp /mnt/shell/emulated/0/build.prop.bak build.prop
[Update] Here is a copy of my build.prop that matches what the install script expects: build.prop
shell@grouper:/mnt/shell/emulated/0 $ sha1sum build*
48f7593c2ff2fa85a147639fd7b77c3bc0607249 build.prop.bak
Now to get root back...
[Update]
Getting root back on my Nexus 7 was easy enough that I didn't mention it earlier, but a few people have asked. I pieced together the steps from this Google+ post and part of this XDA thread into hopefully a clearer walkthrough, if this helps anyone. You could use TWRP instead of CWM, but CWM worked fine. Note that this is for the WiFi Nexus 7 (grouper) and there are different downloads for the GSM / 3G version (tilapia).
1. Download SuperSU from here and copy it (I used adb push) to the Nexus 7
adb push ~Downloads/UPDATE-SuperSU-v1.43.zip /sdcard/
2. Download the latest CWM recovery from here
3. Flash CWM recovery:
fastboot flash recovery recovery-clockwork-touch-6.0.2.3-grouper.img
4. Reboot into CWM recovery and pick the "recovery" option
5. Flash the UPDATE-SuperSU-v1.43.zip file from /sdcard
6. When the device reboots, if it asks if you want to disable flashing stock recovery, answer No.
You should have root back.
[Update]
If, like me, you have the same issue updating to JWR66Y from JWR66V, here is a forum post with the right debuggerd.
I also had a permissions error (set_perm: some changes failed) but following this post, I unrooted before applying the update (using CWM) and it worked.