The Bankers Special was made in .22 Long Rifle and .38 Colt Police (aka Colt New Police, aka .38 S&W). The cylinder is too short for the .38 Special. Colt's ads say "The Banker's Special is especially adapted for use by bank employees and others whose primary requirement is for a Revolver of small size, all around dependabililty and absolute safety. The United States Government has equipped its railway mail clerks with the Colt Banker's Special."
Colt ads indicate that the first guns were in .22 LR and available with wood stocks at $28.50, with pearl stocks at $37.00. They were made on the old Police Positive frame, not on the newer Police Positive Special frame which has a longer cylinder and cylinder window for use with the .38 Special.
On the barrel marking, I am going to stick my neck out (it has been there before) and say that the barrel was replaced by Colt in the 1947-1955 period. They put on a barrel with the (then) current company markings and the current front sight style.
Note that there is some misunderstanding on that 177000 number. That is the starting number for the PP series for 1928, not the starting number for the Banker's Special alone.
Note also that in Colt's case, the terms "round butt" and "square butt" are not as clear cut as in other makes. The square butt is quite sharp, but the "round butt" (as in the pictured gun) would better be described as rounded off; it is not a "round butt" as in S&W revolvers of that description.
The grips pictured are not original, of course. They are plastic Franzite grips, where the original factory grips would have been checkered walnut (or pearl).
Jim