Perhaps I should write a group undeleter then?

Yeah, it's pretty sneaky.

It's been a while since I looked at Push-To-Test.  I seem to remember that entering PTT mode deletes a lot of your variables, but perhaps not all of them.  So now I'm wondering if there's anything (other than modifying the OS) that you could do beforehand to guard yourself.  Does it disable hooks in RAM?  Does it disable ONSCRPT and OFFSCRPT?  What about creatively-corrupted VAT entries?

Hm... Hooks are definitely gone. Going to the PTT menu and quitting without entering PTT mode kills all hooks anyway.
I'm not sure about your corrupted VAT entries, nor ONSCRPT and OFFSCRPT.

It brings up a menu from which you can start PTT mode.
It disable all apps and programs and prevents you from creating new ones. It also deletes all groups.
You end it by receiving a variable.

Install a patch. Several are on ticalc.org
We're discussing the scenario of if you don't have a link cable and how to possible work around it. (So far, no luck. )

Turn the calc off. Hold down left and right while pressing ON.
If it doesn't work, your OS version is too old or a patch is already installed somehow.

I made a program that installs a counter push to test sequence. Up Down ON uninstalls it.

Umm... I'm not sure that this is the best of ideas, but here are all the programs that I have made that patch the OS:

-AboutFix: OS 2.43 Puts your name in the about screen. Re assemble it unless you want it to say "Owner: Brian Coventry"
-Addr series: OS 1.19, 2.43, 2.53fixes ERR:Bad address when grouping and ungrouping
-ChkSmFix: OS 2.43 Fixes the OS checksum (only necessary for 2.43 fixes)
-Mod253: OS 2.53, my pride and joy, Un PTT (UP DOWN ON), PTT deletes require [stat] also, about screen (be sure to recompile with your name), give back classic ram clear screen, fixes ERR:Bad Address, and PTT doesn't delete groups
-NoDel series: OS 2.43, 2.53, PTT doesn't delete groups
-UnPtt 1 and 2: OS 2.43, Run both to allow Un PTT with (UP DOWN ON)
-Versn series: OS 2.43, 2.53, Fixes error version on groups.

-Write flash templates: I'm feeling generous, don't make me regret it.

Some of these don't have OS version checks, so be sure you are doing it on the right OS.

Nothing you can possibly do will fix it because it is stored in the certificate. A full mem clear won't do it. Even a delete OS, run flash test, reinstall operating system won't fix it. I guess the only thing aside from properly fixing it would be to delete the certificate.

However, PTT does have one fatal flaw, it doesn't disable OFFSCRPT. Which means, put bcall(_removeAppRestrictions) in OFFSCRPT and never worry again.