There are roughly 100 pages spread across multiple posts discussing prewar Schwinn serials. The one thing consistent about the charts that are out there is... wait for it.... they're inconsistent.
This is due to a number of circumstances but mainly stem from manufacturing millions of bikes and selling them private labeled through distributors. Most manufacturing systems will still utilize parts manufactured in previous years until stock runs out. I see this all the time with vintage guitars.
Date stamps, serials and specific parts can be great indicators of manufacture date but there will always be outliers. One thing for certain on your bike is it's not a '35.
One chart is pretty specific about A serials with linear, closely spaced small digits.... Yours seems to fit that description and with a '37 crank that seems likely...
On the other hand it's possible it's late '38 early '39 with leftover crank.
As for model you got me... maybe a BC?