If you're using a script to do so, make sure it's handling API limits specifically for "edit" calls. I realized after I tried overwriting mine that it was quietly skipping a bunch of comments, presumably because there is (allegedly) a 1 edit call per 5 second rate limit. Since adding a 5 second delay between each re-write, it seems to be working for me.
I ran into this issue with u/j0be's Power Delete Suite, I ended up writing my own script to do the job.
This happens with PowerDeleteSuite's main version, but one of the forks has a 5 sec pause between deletes that does work. It's very slow (~1000 comments edited in 2 hours), but works reliably. https://github.com/deestan/PowerDeleteSuite
This userscript will manually overwrite comments manually. You go to your comments page, scroll until there are no more comments to load, and run it. It'll go 1 by 1 - edit, new text entered, save, 3 sec pause. By default the replacement text is a link to the script, but you can just edit that to be whatever you want (and you should edit it to make it harder for Reddit to batch restore). https://greasyfork.org/en/scripts/468337-so-long-reddit-thanks-for-all-the-fish
Note 1: Method #2 doesn't use the API, so should still work on July 1. PDS does use the API, so might not.
Note 2: Both methods allow you to continue to use the browser in another tab or window (at least in Firefox). Some browsers and extensions will suspend or unload tabs if they haven't been viewed in a while, so best policy is to do this in a separate window.
Note 3: The default PowerDelete Suite should be fine for exclusively deleting comments if you run it several times. Just keep running it until nothing shows up under comments. To be sure, once your comments are all gone, wait an hour, and check again. If anything remains, use method #2.
(Overwriting account #7 right now! Using PDS with 5 sec pause has worked flawlessly.)
Yup, I could see Reddit noticing a large number of comment edits and bumping that timeout higher.
Also, many users probably don't know what forks are and might just run the first version of PDS they see, see that it isn't "working", and give up or wait for an update that never comes. The userscript is easier to understand because it visually performs the same actions a person would take to edit comments. And it's more fun to watch than PDS's progress bar. :)