First of all, let me start with saying this is not best practice. You may know yourself that this can lead to problems if e.g. your PC goes blank or you want to give one project to another person for development. Of course, especially as a one-person-endevour, there are more important things than having test data importers and stuff :) So let's look for solutions.
NFS Permissions
To get NFS permissions right, your users need to have the same UID and GUID on host and guest. It's pretty tricky to setup and you should not change it from the guest. Maybe you can change it on the host to make it writeable to mysql and make UID and GUID the same. Of course, the moment the host changes this won't work anymore.
rsync shared folder
Rsync might not be the fastest in terms of syncing, but if you create on rsync shared folder where only MySQL is writing and which syncs back to some folder on your host this might be a solution. The "real" projects could still live inside a virtualbox share or nfs and you don't need to bother with correct permissions.
There might be some other solutions as well:
Create a backup/restore strategy
One way to go would be to backup MySQL inside your vagrant box at various points, e.g. every day. You could also run the backup when the box is shut down, thus creating a backup right before you destroy the box. Placing this backup at a shared folder, you'd have up-to-date data in case you destroy a box. Performance should be pretty good as the data MySQL is using wouldn't be on a shared folder.
Run MySQL on host or other vagrant box
It's of course possible to connect from within your vagrant box to your host or another vagrant box which runs MySQL. Your host or this box could be long-lived and could serve as a central "MySQL Server" for all your projects.
Have a MySQL slave running on the same machine which writes to shared folder
I believe with MySQL a master/slave combination is possible. Running both on one machine with the master (which you use in your projects) living inside your vm and not writing anything to a shared folder and a slave which writes to your shared folder and is a mirror of your master. This would mean that you have high performance and a few secs of delay between writing something and having it written to your shared folder. Of course, keeping this setup running and making sure it works all the time can be tricky.