A typical smoke detector has about 1 microcurie of Am-241. Am-241 is an alpha emitter and you can use it produce neutrons (about 70 neutrons per million alphas with an Am-Be source). If he had 100 smoke detectors (about 100 microcuries) he could have produced 260 neutrons per second. That is enough to do, well, pretty much nothing. When he was going to join the Navy he should have tried for the nuclear program. Then he would know how futile his experiments really were. Well maybe that is not such a great idea. It wouldn’t be pretty to see what would happen if he got his hands on some radiography sources or ‘real’ neutron sources.
Also, part of building something well includes not stealing the parts.
Perhaps his engineering future includes rock-splitting.
As I understand it he was also scavenging Th232, which will fission with fast neutrons. Over time, the hot daughters add to the flux. Putting something in a garden shed and walking away could accomplish this, given enough time, even considering the low neutron collision rates.
The amounts of detectable radiation, and the distances involved from which they were read implies something was escalating, because the amount of original material could not have accounted for it. Also, in the original story, he had found a big jar of radium luminous paint stored in an old clock in a pawnshop, so he was not limiting his alpha sources to the tiny smoke detector gleanings.
All that work, and he must never have read a book...Darwin on the Installment Plan.