I think you can leave them in the fridge for next spring. You may have to change the vermiculite if mold starts to appear.

If you don't mind me asking, how did you stratify those peach seeds? I have some in the fridge in soil in a baggie, and also some more in the fridge just moist in a baggie and they don't seem to be doing anything. What did you do to get roots? Any help you could give me would be very appreciated.
Lynn

Nothing fancy, really.. I put them in about 6" of damp vermiculite in an airtight plastic tub at the back of the fridge. The original pits were fairly small and kind of soft, so if the ones you try are exceptionally hard it might be worth soaking it first or filing an edge kind of like you would do for an avocado seed.

Okay, thanks. I will give it a try.