I believe that "E" serial number prefix might indicate the middle-1920's; (but I already hinted at 1920's!). The tubing and joints may look unfamiliar, as it was a 28" wheeled bicycle which used tubeless tires; and old bikes with obsolete tires do
not seem to survive for very long, in any great quantities. So, you may be more familiar with the tubing arrangement and joints on a smaller frame, or just newer bicycles? It seems that Sears catalog sales may have been slower than others to adopt the smaller "kid-size" for kids' bicycle toys.
Perhaps you might investigate the head tube to see if it reveals any head badge fastener holes. If it has vertical holes a little over 2" apart, then the bicycle may have been badged as an Elgin. If closer to 3" apart, then maybe Excelsior's own red "E" badge. Hope this helps a little.
There are lot's of different Excelsior's out there and hopefully I can document some of these different companies and fill in the time lines of the what they built and or sold. Excelsior Supply Co of Chicago was the founded by George Robie. Here are some clips from a 1903 Motor Magazine...
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