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I'm new to qubes, so excuse me if I may sound stupid, but wouldn't it be easier to include your storage space in your overall qubes setup (maybe as an LVM), so that you would just use your qubes and extend their personal disk space? This way you could take advantage of the isolation provided by qubes without the hassle of setting up a dedicated storage VM which would also need to check permissions.
On the other hand you could probably set up a storage VM and serve the files via NFS on a IP basis. Since every qube has a unique IP address you could make sure that no other qube except the one you permit has access to a specific storage folder.
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