Herewith the fraught CCleaner journey of the addled elderly, and a happy ending.
You will look in C:\Program Files\CCleaner (and scour every corner of your computer if you’re me) for the elusive ccleaner.ini. You will not find it.
At which point you’ll recall a passage from the support pages:
“All CCleaner INI files must be located in the application installation folder (typically, C:\Program Files\CCleaner). By default, none of the INI files exist when you first install the application.”
Ahhh, you'll think, no INI files exist when CCleaner is first installed, but since I installed CCleaner years ago, maybe INI came and went. Maybe I'll uninstall and reinstall CCleaner. Maybe a new installation of CCleaner will "discover" the second Firefox profile, and I can bypass INI fiddling altogether. Or maybe running the new installation half a dozen times will cause a new INI to materialize as if by magic.
Fast-forward: Nope.
By this time hours have elapsed, and being no closer to a solution, I’m ready to bail. Then I spot a small UN-ticked box in the Options > Advanced screen. “Save all settings to INI file,” it says.
Bingo! After ticking the box, I go back to C:\Program Files\CCleaner, and there, big as life and twice as ugly, is ccleaner.ini.
After adding this line to the file…
CustomLocation2=FIREFOX|C:\Users\MyUserName\AppData\Roaming\Alternate Firefox Profile
....I can confirm that CCleaner is indeed cleaning the new Firefox profile. Hooray!
The takeaway is that to conjure the mythical INI, the all-important “Save all settings to INI file” box must be ticked, because it is not ticked by default. (Forgive an old person’s silly question, but…why isn’t it?)
Thank you all for your support. Am pouring a stiff drink and going to bed.