In Picard you can go to Options > File Naming and then tick 'Move files when saving'.
There's some other fields in there that you might want to look at, here's a screenshot:
In short, yes Picard can do it, but you'll probably want to mess with some settings to move all the file types you want and to name the folders correctly/match your naming conventions (this will involve scripts if you have a preference).
But please be careful and start slow - searching 300gb's of music for 100gb that's been incorrectly merged in all at once would be a real headache
Well, I Picard and MB, so I reckon just run it all through Picard anyway, but maybe it would be best to make a new Music folder, run your 100gb of new music through Picard and into there (instead of your old folder).
If you like the results, do the other 300gb into that folder as well.
And if you can't be bothered/you don't think it was worth it, just copy the 100gb into your existing music folder instead.