You don't actually have to set all the modification dates to now, you can pick any other timestamp you want. So to preserve the order of the files, you could just have the script sort the list of files by date, then update the modification date of the oldest file to some fixed time ago, the second-oldest to a bit later, and so on.

You could even exclude recently-edited files because the real modification dates are probably more relevant for those. For example, if you only process files older than 3 months, and update those starting from "6 months old"^1^, that just leaves remembering to run that script at least once a year or so. Just pick a date and put a recurring reminder in your calendar.

^1^: I picked 6 months there to leave some slack, in case you procrastinate your next run or it's otherwise delayed because you're out sick or on vacation or something.

Have you…called attention to this at all?

Have a script that makes a copy of all files that are 1.9 years old into a separate folder.

Create a series of folders labeled with dates. Every day copy the useful stuff to the new folder. Every night change modified dates on all files to current date.