Your first instincts were likely correct, regarding the 1947-48 'D' CWC bike. It may have worn a CWC badge (e.g., Roadmaster), or another retailer's label.
The 2 pictures of pre-war examples of different designs (size and model) did help confirm that it was unlikely to find pre-war examples of the same design, same details.
The 3 other bikes look similar to yours; one may be a 1946-47 'C' and the others had words attributed, like "mimics" and "Shelby" and "Schwinn".
The bike on Worthpoint is most likely
not pre-war, nor 1930's, (nor Shelby, nor Schwinn); and those are
not Worthpoint's words, but those of a seller on a website, punctuated with a question mark (?). It is common when guessing at a bike's age to arrive at a general range of 'no-sooner-than' and 'no-later-than' dates. The last refurbished bike pictured from 2013
might be earlier post-war, such as ~1946, inferred by the seat post clamp, (which is hard to see). Often there is less info or fewer examples of girl's, juvenile's, and youth's bikes; (and sometimes those models did not get the investments for designing newer styles). For more serial number info see the following site by a CABE member:
https://vintageamericanbicycles.com/index.php/cleveland-welding-co-roadmaster/