I didn't think I had seen that sprocket on that frame, but I found a couple more examples. Sounds like Snyder/Hawthorne/Rollfast intermingled more than I thought.
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The Hawthorne I've got with that sprocket is a Double Bar Roadster(taller seat tube than the last photo).
Your frame is definitely H.P. Snyder built. Since it looks like you've got patience from cleaning the rims, I'd recommend using a dull pick or something of that nature to dig the funk out of that serial number. Maybe lightly apply some WD 40 and steel wool to bring out the edges of the number.
I just hate when I see people that take what looks like a die grinder to a frame so they can "see" the number better. Great, you can see that shiny bit from space now too....lol
end rant
I can't remember if the top 3 numbers/letter are the model on Snyders, or the year. I need to go look at mine.