Hey!
Current version of player does have limitations on how much data it can store. The limitation is not set by me, the browser sets the limitation. (But it should be 500 MB I think) The new version I am working on will allow you to specify the exact storage limit. But the new version is more than just a few days away. I can't promise on when the version will be out. As for organising, if you can bypass the storage limitation, I don't see why it should have any problems organising that many songs. The new version will have some new features for organising, but currently your only problem should be the storage limit set by the browser. The next version should solve your problems, but again, I can't give you any hard numbers of when it will come.
If you are more technically oriented then this info might help you. The app uses file system API. And browser puts limitations on how much data the API can use. There is a storage quota API that will allow me to let user manage the storage, but if you can change the code, look for filesystem initialization and try increasing the size specified there.