My wife is somewhat geeky and spent all of college and grad school working in retail jewelry. I'll let her say what she's come up with:
I know you like the Ir as a symbol of permanence, but remember that a ring was first used (as opposed to say a necklace) because it never begins and never ends. That said if you'd still like to do Ir see if you can have an infinity symbol fashioned from it and then inlay it in another softer metal, this allows for minor resizing and emergency removal.
If you want to stick with a band, I distinctly recall one wedding band company that sent us materials that would cast your ring with the DNA bar things (what ever they're called) from your genes, it looked like a rather abstract pattern, but has meaning for the two of you.
If you want a man made diamond, LifeGem can make a diamond out of human hair, it actually has more carbon than ashes do, so you can usually make one from less material. But you'll probably want to save hair clippings for a bit, and it'll take 3-4 months to make, so this may not be in your time frame.
If you'd like to have a more traditional diamond; I'd suggest getting one of the specialty cuts. Many of them are specially engineered for light, brilliance, and even shape. They also have reports, certifications, and laser inscriptions on the diamond (personalized laser inscription is also something you might consider having done)
What ever you pick just keep in mind that if you get a set the wedding and engagement rings must be of the same metal or the softer metal will be worn away by the harder.