I've determined from various conversions that microfasteners is the only one that has small enough screws - #0 x 3/16th ~ 1.5mm dia, 4.7mm(ish) length. Any longer than that and i'll go through the wood on the springback.

They come in packs of 100 so I'll see about ordering some and shipped here, then once they're here, anyone else needing some of these annoyingly tiny screws can get some off of me