Coming from a jeweler’s perspective I’d say always start with the jeweler, but I may be a bit biased hahaha

Even if they can’t come up with the design you’re looking for, hopefully they can at least explain the limitations for such a design. From there you could have anyone with an eye for mechanical stuff take a crack at it. If you could get a 3d model of all the parts, modern casters will just print it in lost wax and cast the parts for you. Ideally the jeweler sets that up for you.

The biggest expense should be the casting. Gold is the highest it’s ever been right now, I’d recommend 10k yellow or 14k white for the strength. The actual assembly will probably be a little pricey, but a good jeweler will work out a cost by pricing individual welds and whatnot. “Assemble this custom one off ring” sounds like it should be a hugely expensive thing, but if it’s just 5 welds and a couple hinges, realistically that would only be a couple hundred as a repair job.