(1) Consumer Financial Protection Bureau (CFPB): http://www.consumerfinance.gov/complaint/, and,
(2) New York State Department of Financial Services (DFS): http://www.dfs.ny.gov/consumer/fileacomplaint.htm.
This will make it more likely that you see a favourable resolution. Further, this assists due process in identifying and resolving problems in our financial system.
if they were holding your money without a schedule of release, that would probably be a stronger ground for a complaint.
Further, when consumer finance issues come up in D.C. or Albany it is these complaints which inform the debate. Having no documentation means regulators flying blind.
(4) If you research any other POS's reply here so I can see. ;)
That's the shakedown the GP was referring to. The BBB is a scam.
I found it very surprising that Square doesn't provide an alternate method for identification, it's mind boggling even. Something like Instant Bank Verification (similar to what mint.com or venmo does) would be a good alternative and carries no additional overhead for Square.