Is this gmail by any chance?

I use Hover, which provides a standard IMAP system.

I'd go about it by using filters to move messages to specific directories in Local Folders on receipt. I'm not sure that setting an IMAP account's folder to reside inside Local Folders will achieve what you want; I'd suspect that it will simply reposition the local folder yet keep it linked ("synchronized") to the IMAP account.

OTOH, moving messages to Local Folders will detach them from the IMAP account, and cause them to be removed (deleted) from the IMAP folders, both locally and remote. You could copy instead of moving, but then you'll have two of everything.

From where you are now, this means creating those folders under Local Folders then moving messages by hand. In my experience, block-select, right-click, "Move to" is safer than drag'n'drop.

I have to say that Archiving under Local Folders needs a bit of patience and fiddling about, as it seems to think that the account's Archive should be in the IMAP folder hierarchy.

In moving messages, it should remove them from the IMAP account's folder (that is the intent). Filters are not acceptable as I am wanting to do this on a one by one basis, after reading the emails (filters only run bulk manually, or upon receipt).

The problem I am having seems to be what you reference in your last sentence. When I archive, it usually moves the emails into the Archive on the IMAP folders rather than what I want, which is to remove it from the server and place it in Local Folders.

My intent is to reduce load/storage on the IMAP server and increase the responsiveness of Thunderbird when searching for emails throughout archives.

I like keeping all my emails, so my archive of emails goes back to 2008.

What your doing should work.

I do not have a Hover IMAP account, but the Yahoo offering is pretty standard in IMAP delivery.

I modified the archive to point to the archive on local folders under other. pressed A and the relevant mail appeared in my 2014 archive folder under local folders.

That's definitely why I've been reaching out (option wouldn't exist if it didn't work).

The IMAP server should not actually be even relevant to this process. Hover just uses a standard IMAP server judging by the web interface (it's a common open source interface, I just forget which one).

I think you should try the various safe mode options, there must be something interfering and that will start the process of elimination.

To diagnose problems with Thunderbird, try one of the following:

• Restart Thunderbird with add-ons disabled (Thunderbird Safe Mode). On the Help menu, click on "Restart with Add-ons Disabled". If Thunderbird works like normal, there is an Add-on or Theme interfering with normal operations. You will need to re-enable add-ons one at a time until you locate the offender.
• Restart the operating system in safe mode with Networking. This loads only the very basics needed to start your computer while enabling an Internet connection. Click on your operating system for instructions on how to start in safe mode: Windows 8, Windows 7, Windows Vista, Windows XP, OSX

If safe mode for the operating system fixes the issue, there's other software in your computer that's causing problems. Possibilities include but not limited to: AV scanning, virus/malware, background downloads such as program updates.