If you're familiar with stainless, Ti isn't that different. Go slow, listen to what your tools are telling you. Carbide tooling doesn't hurt, but isn't inherently requisite. Titanium is a wonderful jewelry material (biocompatible, low density, durable, polishes fairly well). It's only "downside" is that it's not expensive. Well-made Ti stuff draws the same attention as higher-Z materials.
I've made a number of Ti rings, but haven't set stones, as the You'll save a lot of time by starting with Ti tubing rather than turning the hole into chips. Depending on the size you need, relevant tubing isn't always available. Anodization is really fun.
I'd check into the biocompatibility of permalloy. Nickel allergies are real and can be acquired, sometimes from rings. Might rust/discolor fingers over the long term too.Laminating a Ti strip to the permalloy might help to attenuate the situation?
Chamfering the inside of a ring isn't hard to do with careful sanding on the lathe. Doing it wrong will amputate your finger or worse -- seek qualified instruction.
The article doesn't make mention of accommodating water/drainage. What happens if a little water gets beneath the stones after a hand-washing?
What a cool and inspired piece of work!