Ring Doorbell Wiring Screws

So living in Alaska it gets cold; here in Fairbanks it get -40º cold. During a -20ºF period of time our doorbell went dead due to low battery, even though it's hardwired to the old doorbell. It was a lower voltage transformer (around 8V it appears), so I upgraded to a larger one. In this I took the doorbell off to check it and try manually changing it, and it being -20º, I didn't want to do all this outside, so I removed it from the mount. No suprise those stupid tiny wiring screws were dropped and lost one completely. I cannot find a replace that works anywhere and Ring doesn't seem to offer them as replacement (but I can find the security mounting screws everywhere online--it even came with an extra one of those). How is no one else losing these smallest screws and losing the ones that are three times larger?!? Anyways, does anyone know where one can find those tiny wiring screws on the back of the Ring unit???