Thanks for the description of your process.
To me, it seems that working on the outside first would be easiest. You just need a concentric, conical stub on the lathe mandrel. Push/drive/wedge the open end of the bell onto that, tap it concentric with a mallet, drill a centre hole from the tailstock and then use a tailstock centre in the argent to keep everything in place while you work on the outside. Then the shape and concentricity of the argent itself is immaterial.
Once the outside is finished, use it to cast a female mould (plaster of paris in a metal tube) that can be attached to the lathe mandrel. Drill and tap a hole in the argent for a drawbar through the headstock (do this as the very last step of outside machining). The drawbar will retain the bell and the exterior mould will support it while you work on the inside.
Brass is good because you can cut it with zero rake tooling. That means a form tool for the inside is a possibility.
Please see from 1:00 to 2:00 of this video for an alternative method of manufacture
What a wonderful film! Cut glass accent and a splendid mid-century adherence to the good old Elf and Safety. I think my favourite is the foundry workers gear - cloth cap and a positive attitude...
To business...The conical stub is actually the route I take for machining the outside. Sadly, any sort of meaningful hole drilled through the argent is not possible for a traditional handbell. Certainly not enough to fix a drawbar. I'll not witter on as to why. For the kid's bells, I am fairly convinced that the cylindrical argent is the solution. That can then be ground down to the traditional argent which is then used to attach the looped leather handle as well as the drilled and tapped fixing for the clapper system. Because these bells don't make a p[art of a "set", they can all be the same size and so I can do much more repetitive production.
I like your idea of a cast female mould. For the kids' bells, I actually do the inside first simply because it is easier to grip the rough-cast outside in my (woodworking) jaws, but for these, accuracy is less important. My jaws won't close down enough to grip the round argent so I haven't been able to try that. I am toying with the idea of a turned wood female socket - especially for the bell metal castings where it would indeed be best o get the outside up to spec - and then tune it from inside. A downer is that, to sound the bell for tuning, it needs to come off the lathe, with all the re-centering problems that this creates.
I think I've got a whole shed load of things to learn about form tools. I'll go, ask My Friend Google...