There is a cutout for one man part 135 ops, or at least there was and all of the things you point out may have been purchased and the FAA is nesting on them. Now if they are in the process of trying to move from one classification to another that might explain things. Or maybe they aren't up and running yet and that is why they are looking to fill the CP spot...
There are lot's of CEO's skimming the cream off the top of the gross revenue of many airlines who had no previous aviation experience...
According to their website,the company was purchased in 2018,and then moved from CRE to FLO!!! They have a guy listed as Dir.of Maint who is an "avionics tech",unsure if he has a "A&P certificate".They show 2 aircraft,both PA-31 Chieftains that are 1977 models(40yrs old),and they are doing charters as we speak.
PT 119 says they must have a Dir of Ops,Chief Pilot,and Dir.of Maint. that the controlling FSDO(CAE),must approve,however,the CAE FSDO has another "bad operator" in CAE,Bankair, from the 1960's,which has a deadly record of killing 20 plus people,many of them pilots,they also DO NOT rate a PT 135 certificate,but they have had one for all of these years,and the reason was a "political payoff",to the late Sen E. Hollings,who greased the track for them!!!!! One wonders if the same thing is going on currently at Air Transport of the Carolina's at FLO!!!!!!!!