How do I keep tiny bead details from turning to mush on silk PLA?

You've pretty much diagnosed it yourself. If the beads in the model are smaller than about two extrusion widths across, a 0.4mm nozzle can't leave gaps between them, so they fuse into a ridge no matter how slow you go. Slowing the outer wall helps with surface quality but does nothing for features the nozzle physically can't resolve. Check the bead size in your slicer's preview or measure the model, and you'll probaly find they're well under 0.8mm.

I ran into the same thing on a chess set a while back and ended up scaling just the detail parts up about 20% in the slicer. Slightly chunkier beads than the 'real' prop, but they read as individual beads from a normal viewing distance, which honestly matters more. If you don't wanna mess with resin, that's a cheap middle ground.

Also, silk PLA does tend to ooze more on tiny features, so even with a smaller nozzle you'd probably be fighting strings. My two cents would be test print one small strip of the beads at a couple diffrent scales before committing to the whole reprint.

This is way over my head but I'm following because I want to print something similar for a friend. If you end up printing the little round bits separate and sticking them on, how do you even line them up right? I'd picture myself gluing them all crooked and it looking worse than the melted blob.

Also does the sticky stuff show through gold plastic? Like if the glue dries cloudy it might ruin the shiny look. Curious what people use for that kind of touch up job.