Bill collectors for CheckSmart and other cash advance joints.

This number and 866-354-0567 (also several other 59xx) calls my cellphone several times a day. Usually starts at around 2 PM Pacific and goes nonstop till around 8 PM every 15-30 minutes.

When picked up or when it hits the voicemail leaves a recorded message call back number with a code, usually the 866 number above or one of the 614-798-59xx numbers.

When called back, the ladies respond as "Corporate Office" won't tell me whose corporate office, or why they are ignoring the Federal do not call registry, they hung up on me when I asked for their company name.

Thinking of calling the local police. Reverse looks shows Buckeye Check Cashing in Dublin, OH

They are only calling you if you owe them money and haven't paid.  They are allowed--anytime, anyplace.
If you don't like it, pay back the money you owe them.

Ummmm. Not sure what state you are in rms, but you a incorrect.  Check your local state laws.  In the state of Ohio if you ask that they not contact you at a certain number (such as a work number) the calls must stop.

Yes, Buckey Check Cashing is a know violator of fair collection practices.  I have recieved the many and repeated phone calles even days after paying in full.  Sometimes even  10 phone calls day, (5 pairs of 2 about 20 seconds apart).  They Need to be reported to OHIO Attorney General, Better Business Burseau and the "FSPSA or what ever that association they belong to and advertise on TV and in their Stores.