Creating a new catalog like this is not really possible -- you will lose your virtual copies and adjustments and collections and keywords and everything else you have done already in LR.
Furthermore, re-organizing folders like this is, in my opinion, the wrong direction to go in. To be blunt, in my opinion such a re-organization of folders and folder names is a sub-optimal use of your time. You would be better off putting this energy into developing a good set of keywords and captions for your photos, and use those instead of folder names/locations for your organizing and searching.
I use a similar format but do not create a folder for each month. The format you want is available as an import option but the final folder will not have just the DD. I find having a longer name on the date folder is a nice safety feature when I use the wrong import. I copy my photos to an external backup drive as part of the import and the full YYYY-MM-DD is useful for this.
I redid my photo directory recently. I created folder from LR (right click on the disk/folder where you want the new folder) so LR shows it. You can drag all the individual day folders as groups to the new folder just do it in LR. I was using external disks so it took a few minutes to process but on the same disk, it should be fast.
Thanks for your input.
As there seem to be no automated way of doing this, I took on the task to reorganize all folders manually.
I kept to my original target structure of YYYY \ MM \ DD. I started on the current year and am now working my way back to 2003. Oh yes, there is some serious amount of clicking and dragging involved, but at least I know what to do in the evening for the next few days