Webelos hanbook:
P4 - Your son has joined the part of the Cub Scouting program of the Boy Scouts of America that is for fourth- and fifth-grade boys.
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If a boy has completed third grade, or if he has not completed third grade but is 10 years old, he's the right age for his den.
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Most Webelos Scouts are in this program for 18 months.
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...and after he has completed the fifth grade and is at least 10 years old, or is age 11, or has earned the Arrow of Light Award and is at least 10 years old.... Boy Scout.
I stand corrected (re: Webelos I vs. Webelos II), three months for Webelos emblem, six months Arrow of Light. Start pushing it in June right after school gets out and I guess you could ram the entire Webelos program down the boy's throat in as little as nine months.
Your boys may be different, but if I was in a Boy Scout troop I would be rather leery of an entire den bridging over in 9-months. The exceptional one or two, sure.
Most do not have the emotional maturity at 10 years old - in the middle of 4th grade - to be in Boy Scouts.
Your situation may be unique in this regards. But, from my armchair, I think you are doing the boys a disservice by pushing them.