Is there no transparent substance that is gel-like for a period of time before it cures solid so that the pieces can simply be suspended in it and nudged to their final positions manually? Like a gel suspension 3D printer but where the gel hardens instead of being washed away at the end. https://www.youtube.com/watch?v=swB5-GzX3nQ
I don't know how viscous SLA 3D printer resin is, but if it could be made viscous enough then it seems like maybe you could just suspend the parts in it, tweaking their positions as much as you want until they're just right, then blast the whole thing with enough UV to cure all of it.
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