Multiple Editing Of Filenames

Hi all,
I'm a bit of a Newbie, and need some help re-tagging my 1000's of mp3s. I'm usually quite good at figuring things out for myself, but now I'm stumped.
I'm wondering if anyone knows if there is a way of editing a file which shows artist/title, and splitting it so that the "file" will show the title, "title" will show the title and "artist" will show artist.

What I have:

file current: 1 - Sonny J - Can't Stop Moving (Mirwais Remix)
title current: Sonny J - Can't Stop Moving (Mirwais Remix)
artist current: Sonny J
album artist: Various

What I want is:

file new: Can't Stop Moving (Mirwais Remix)
title new: Can't Stop Moving (Mirwais Remix)
artist new: Sonny J
album artist Various

I tried uploading before and after sreenshots to show what I meant, but they wouldn't upload for some reason. Hope my listing above helps explain to someone out there.
At present I'm cutting and pasting the artist from the file name in the left hand panel, which is rather laborious. Once I've changed things to the way I want them I use "$num(%track%,2) %title%" from the Tag-File name drop down to change the file name to the way I want.
If there's a quicker way of doing this, I'd be eternally grateful.

Here's an example how to split a tag field into multiple fields:

Hiya Dano,
Apologies for time in replying. the solution you gave worked spot on, saving a lot of time. So many thanks for that.