First off, no, I've never had to get a carbon ring out. Mainly because I don't shoot cartridges/powders that seem to develop them. I've read about them a lot, but have never seen one myself (yes, I do believe they exist).
Be that as it may, I'm kind of stunned that you can't locate a fixed handle pistol rod in .17 caliber. Took me about 30 secs...
Amazon product ASIN B008CXQ2A4
Honestly, if it were me, I'd just buy a cheap .22 cal rod, saw off the handle, file a flat on the butt end, and affix a handle via a piece of metal with a .22 cal hole, and drill and tap a set screw to keep it in place. This doesn't seem like rocket science to me, but maybe I'm just used to having to fabricate stuff, when it seems no one makes what I want. As to the bushes, again, I'd take a .22 brush and some snips, and snip one end of the brush down the the diameter I want/need.
But perhaps I'm just too simple a person to figure all this out...