Update: I have been able to fix the problem. Spreading the legs on the bolt worked. I had to try it a couple times to get it right. The first time I over did it and made it so the leg on the hammer cam never actually dropped off, so the cylinder never actually locked at all. That's clearly bad. A small correction the other way put things in the correct position. The cylinder now spins at half-cock and locks in correct time.
On a whim, I bought a spare parts set for a Pietta 1851 in the hopes it would fit in case spares were needed (nobody seemed to know who the actual manufacturer of this pistol is). The current Pietta spares don't fit. A couple thing physically fit in the slots, but nothing works as it's supposed to. So, in the future if this thing bites the dust it may just become a wall hanger and get replaced with a new one. I learned a ton in this small process, but I'm gonna leave working on these to the pros. I hope to enjoy it safely til then.