See SFO777's rather excellent trip reports on JetSmarter. And there's a few on Jetsuite as well. And there are many more empty legs on the market than just those two online apps- just at higher pricing.
I'm not sure I really care that much about a 4 seat light jet, other than just as a bucket list thing. But then, the only legs that have come up at MSY are routes already very well served commercially, like MSY-DAL.