Hooray! A kindred spirit in the realm of baby-raising! I think that long-term nursing and attachment parenting really helped set the stage for my boys' good health, and for our strong relationships now, as well as for being the good young men they are becoming. (sorry, I'm a bit sappy this morning - I just dropped the younger one off at high-school orientation, and it's one of those "my babies are growing up!" moments).
The only thing that ever worked consistently for my guys were the Highland teething tablets, but it sounds like your little fellow is spitting them out. Have you tried dissolving them in a bit of water and dripping it in? (no idea if it would work, but it might be worth a try)
I haven't heard anything about amber as a teething object, but it makes sense that it would be soothing. You would probably want to get beads that are a good size, not "chips." Make sure that they don't have fracture lines, because amber is not a very hard stone and kids do have sturdy jaws. I would hate for a bead to break and choke your child. (but I wouldn't recommend any harder stone because then you're putting little teeth as risk)
I'm thinking that you will want to knot the strand between each bead. This will prevent you losing all the beads if the strand breaks. Not sure what sort of closure you would want to use. I would avoid a necklace because of the possibility of strangulation. If you're in Indianapolis, I suggest visiting Bead Angels in Broad Ripple (65th & Ferguson)for some good assistance. Be sure that whatever you string the beads on is non-toxic, and won't become brittle from being wet frequently. Also that it won't become a germ-magnet from being wet all the time.
You might also want to consider just using one or two beads, I'm thinking here about the cost vs. the risk of losing the teether. It's one thing to lose something you spent $2.98 on, and quite another to keep replacing $15 or $20 worth of amber each time it gets lost.
I know that my guys had the old-fashioned teething rings/bracelets with hard rubber beads (you can still get them), but I don't really recall that either of them really chewed on them. They are too big for a bracelet, and too small for a necklace, so they have to be held in the hand or attached to something (like a car seat? sling? Mommy?) so that they don't get lost.
Good luck!
D.