Based on this, I will go with the upgrade process on a new instance, just to make sure everything goes smoothly. Here's what I've got from your notes:

1) Yes, current MLF version is 2.0.2. And yes amazingly, hosting plans (cpanel hosts at the very least) still allow use of PhP 5.6. It's not supported, but can still be used.
2) Port existing site and DB over to new instance. Update config/db_settings.php to reflect new DB settings.
2) Upgrade to 2.3.5.
3) Upgrade to 2.4.24.
4) Switch PhP version to 7.4.
5) I know that we have at least a few duplicate email addresses, so I will clean up the DB before proceeding.
6) Upgrade to 20220803.1 (2.5.4).
7) Switch PhP version to 8.0 / 8.1.

All necessary releases can be found at: https://github.com/My-Little-Forum/mylittleforum/releases

Our current version of MySQL is 5.6.51. The new instance MySQL version is 10.3.38. My understanding is that both versions should work through the upgrade process, but I'll perform the upgrade on the newer, 10.3.38, instance.
If I run into any issues with the last upgrade, I'll take another look at the "Problems with the upgrade procedure from 2.4.x to 2.5" thread.

I've had a heck of a time exporting the data from the existing instance / DB, as either the script or DB is timing out before the export is complete. The entries table has 500,000 records and only 300,000 records could be exported before the timeout. I've got a piecemeal solution we're going to attempt today that should work.

My one question at the moment: I thought I read on the forum that there was a problem with new DB tables that wasn't fixed until the upgrade script in 2.3.7 (and not 2.3.5). Is this anything I need to worry about, or will that simply get fixed with the upgrade FROM 2.3.5 to 2.4.24?