I personally haven't used the ring before so I haven't had the exact same experience with that... but I did have a tampon issue once. It got really far up in there and the string broke. I needed about 1/2 also but I just couldn't get it out. I also tried and tried in different sitting, standing, laying down positions - nothing worked.
I finally realized that I either had to find something to get it out with or have someone else help me (which was pretty much a last resort). So I took a pair of small tongs (gross, I know, but it worked)... got them in there and pulled out the tampon.
You can probably do the same thing with a ring. Just make sure you get a small pair that will fit in there. And if you're against that idea (it's weird, I know) then have someone help you.