If you're going to use Lightroom to achieve some sort of "organization", in my opinion you would be much better off using keywords and other metadata to get the organization you want, and leave the folder structure however it is now. Once that is accomplished, you can use the keywords and other metadata to do your searching, and not worry about the folder structure, in fact you can pretty much ignore the folder structure. Keywords and other metadata give you a much more robust and powerful set of organizational tools, in fact, you can organize photos so that they have multiple keywords and multiple metadata, but if you use folders for your organization, photos can be in only a single folder. (This is only one of many benefits of using keywords and other metadata, but its a big one).
If you must re-arrange the folders, a very sub-optimal choice in my opinion, then you have to do so manually. Move or rename photos and folders to wherever you want, doing this move or rename entirely in Lightroom. There are no global folder re-organization methods in Lightroom.
I also can't understand how 2015/March 22 is a better system than 2015-03-22, seems to me you are thinking of doing lots of work to change one text string (folder name) to an equivalent text string (folder name). In fact, if you use 2015/March 22 you won't even be able to sort your folders in chronological order.
I agree wit dj_paige in that just changing the number of the month to spelling it out would be a step backwards.ARE going to do it,
Although, if you do decide to do it, rename them from WITHIN LR, and the folders should correspond to the structure you have modified INSIDE LR.
Also keep in mind that the following characters are allowed on Mac OS X, but not on Windows:
\ / : * ? “ < > | [ ] & $
If you ever need to share or open images on a Windows system all of the folders will have to be renamed!
IMHO, what you have now (YYYY-MM-DD) is perfect! One of the biggest issues we see in the LR forum is caused by users changing folder and file names. As long as it's done inside LR and not with Finder or Windows Explorer there is generally no issue. The problem here is that there is no folder batch renaming tool in LR.....and as explained there's no benefit to changing your current folder naming convention.
I can recommend this book by Peter Krogh for more advice on organizing your photos in LR: