From the OP:
Quote Originally Posted by Solipse
...If I switch to carpenter and open up my synth menu and stick two, three or more crab bows into my synth box, I can attempt to fuse them together into a higher quality version...
This means that I just grind out a ton of NQ bows then synth them all together until they are HQs. This means that I don't need any HQ mats to get HQ goods. This means that HQ goods are essentially worthless; no one ever needs them for anything.

The whole problem you're trying to address is essentially the elemental staves market problem in XI. I don't think your proposed solution would work out as perfectly as you think.