I'd un-frame them and store them flat. 10 years from now you may wish you had something from this stage. I regret most of what I've tossed and slides don't cut it (though digital images are a bit easier to look at/remember from.
The flat files were all full too. Sadly I can't store physical work in a "cloud".
The saying is that cleanliness is next to godliness, but STOP! Don't toss! Do what John suggested and store.
Not sure about godliness, but being tidy sure helps my OCD. :-)
110%.....DO WHAT JOHN SUGGESTED!!!!!!!!!