Can "preferentially" be used as an adverb of the word "priority"?

Question

I have searched an adverb of "priority, prioritize", but have not found it yet. Instead, I have found the word "preferentially", which is an adverb of "preference, prefer".

As far as I consulted my dictionaries, "priority, prioritize" and "preference, prefer" differ in meaning a little. Can "preferentially" be used as an adverb of the word "priority, prioritize"? For example, does the following sentence I created make sense?

Music data is given priority over text data so that the system preferentially stores music data when available storage capacity is not enough.

Answer 1

Yes, that's a nicely written sentence. It's both prettier and more concise to use preferentially here; the equivalent with prioritize would be this:

Music data is given priority over text data so that the system prioritizes the storage of music data when available storage capacity is not enough.

That's ugly, too, since the use of both priority and prioritizes sounds redundant.

I would, however, substitute insufficient for not enough, or do something like not enough to handle all incoming data. Not enough on its own is a bit stylistically inconsistent IMO.