How do you keep a wire wrapped piece symmetrical when both sides start drifting?

Paper template, absolutely, but not just one. Trace the half of the design you like best, then flip it over and lay the wire on the flipped copy for the mirror side. Eyeballing fails because your brain compensates for small errors as you go, so drift accumulates. I also measure every segment with calipers as I wrap, not afterward. When I did a similar radial piece I wrote the target length for each arm on the template in pencil and checked before I committed the final wrap. If a loop comes out a hair long, don't unwrap the whole section, just take a tiny turn out where it's least visible and re-tighten.

Another thing that helped me was doing both mirror halves in the same session, back to back, while my tension felt the same. Coming back to a piece the next day with a different mood gives you different wraps even if you think it doesn't.

On the converter bar, yes, it's a real thing and it can look intentional. I've hidden a two-part pin stem under a wrapped bail by threading it thru the same wraps that form the bail, so the bail itself becomes the anchor point. Use a bar with a safety catch rather than a simple catch, because a dense piece like that is heavier than it looks and a plain catch will work loose on fabric. Position it so the pin exits through a gap between wraps, not over the stones, and the whole thing reads as part of the design. If your bail is fully closed with no gap, you can add a small wrapped frame behind the pendant just for the bar, and the wrapping style will match the rest so it doesn't look tacked on.

If it still fights you, commit to pendant only and add a bail-side loop. But try the hidden bar first, it's less work than it sounds.

Lurker here, first time posting, so forgive me if this is obvious. I do mostly bead embroidery, not wire, but I had the same lopsided problem with a mirrored cuff panel. What saved me was taking a phone photo of the finished half, flipping it on my screen, and holding the piece up next to it. Errors I couldn't see in person jumped out imediately. Might work mid-wrap for you too.

On the pin back, I once sewed a bar onto a dense beaded piece and it looked terrible til I stitched it with the same thread color as the backing, then it basicly disappeared. Not sure how that translates to wire, but matching materials seemed to be the whole trick. Do you know yet which side you'd want the pin to sit on?

This thread is making me nervous about a bracelet I'm partway through, because I've been undoing the same section over and over and the wire is starting to look kinked where I keep bending it back and forth. Does reusing wire like that eventually snap, or can you smooth it out with the little flat pliers? Mine has faint tool marks now and I can't tell if that's just how it goes.

Before all the fancy calipers came around we used dividers, the old drafting kind, stepped along the wire to check each span. Same idea as a template but you can pick it up mid-wrap without putting the piece down. Worked fine on a sunburst collar I did back in the 90s that took way more hours than yours. One thing I'd add on the brooch part: put the pin on before you finish the last wraps if you can, not after. Trying to wedge a finding into a finished dense piece is where the glued-on look comes from. Built in from the start, it just disappears into the structure.

And for the poster worried about kinked wire, once it's work-hardened and marked up, retire it for practice pieces. No saving it.

A jig fixed this for me. I fought the same drift on a snowflake piece until I stuck pegs in a jig at the six points and wrapped against them instead of my eyes. The pegs can't move, so every arm comes out identical even if my hands don't feel the same that day. Cheap plywood and finishing nails would do the same job if you don't want to buy anything.

Might be worth checking your wire condition too. All that unwrap and redo work hardens the wire fast and it starts fighting you, which makes each wrap a little different from the last. Fresh wire for the final version, practice piece for the first one.

Update: tried the flipped paper template thing and it actually works, the star finally looks even on both sides. Still wrestling with the pin back though. Has anyone really hidden a converter under a wrapped bail, or does it just never sit flat? About ready to commit to pendant only.