Warning--Very Long Post Ahead
They lack the electricity. They also lack the expertise, and it really could not be found for them; what reason does a physicist have to move there?
I can think of no non-ASB way to get Japan a bomb before 1945, even if you push the entire field up 5 or 6 years.
You make Japan sound like a land without scientists. I don't disagree that Japan would have the fewest industrial, and even monetary, resources for competing in a nuclear weapons race, but they had some able talent. Just picking from people involved in the two historic Japanese atomic weapons projects, you have: (borrowing liberally from Wikipedia)
Yoshio Nishina-- He studied at some of the most prestigious European universities and institutions, including
Cavendish Laboratory,
Georg August University of Göttingen, and
University of Copenhagen. He personally mentored
two Japanese future winners of the Nobel Prize in Physics,
Hideki Yukawa and
Sin-Itiro Tomonaga. He is also described as a "good friend" of
Niels Bohr and a "close associate" of
Albert Einstein. Nishina built a 26 inch
cyclotron in 1936, another 60 inch 220 ton cyclotron in 1937, and then in 1938 purchased a cyclotron from the
University of California, Berkeley.
Bunsaku Arakatsu--Also studied at Cavendish Laboratory (Cambridge University), and at Berlin University with Einstein. By 1945, he had managed to complete a design for an
ultracentrifuge, despite the incredible strain on Japanese society caused by the war and allied bombing.
Hideki Yukawa--First Japanese citizen to receive a Nobel Prize in Physics, in 1949. In 1935 he published his theory of
mesons, which explained the interaction between
protons and
neutrons, and was a major influence on research into elementary particles.
Sin-Itiro Tomonaga--Did not technically work on the Japanese atomic bomb projects. However, he returned to Japan during the outbreak of the war, and remained there during the duration of the conflict. From 1937 until war broke out, he studied and preformed research in Leizpig under Werner Heisenberg.
Japan may not have been the powerhouse of science research that Germany was before the war, but they had more than their fair share of important early particle physicists. Furthermore, I see no reason why Japan could not make use of at least some foreign talent. As early as 1931, Nishina invited some Western scholars to study in Japan, including
Heisenberg,
Dirac and
Bohr. If studying with Nishina and other scientists of his ilk was not incentive enough to bring them to Japan, then Japan could've brought them over the same it way it brought over German airplane design talent in the early '30s--by paying top dollar for it.
The way I see it, Japan had one big problem that prevented it from making progress: the Japanese government was slow to get interested in the project. Nishina was worried about the US developing these weapons and using them on Japan as early as 1939, but work didn't begin in earnest until April 1941. After that, you still have the problems of two competing projects, underfunding, and the rest. The US was the only power that was wealthy enough (and geographically isolated enough) to spend whatever amount was needed to develop the bomb. For any other power, funding this project at the level it needs to be funded means a lot less of everything else--less tanks, less ships, maybe fewer divisions. It's a very big gamble to make.
I don't think it's impossible, though. The Empire of Japan in the 1930's had just one foreign policy goal--to make herself strong enough that no nation could challenge her in East Asia. This was seen as the only route to long-term security. If you could somehow convince the Japanese High Command of the true potential of these weapons, they will see that nuclear bombs are the only thing in existence that might have actually get them to their goal. It doesn't fit in with your "just a really big bomb" idea, and I don't think it's too likely, either. But if you can make it happen in your timeline, I think the Japanese government would be willing to pay the price if it could.
Japan already had electrical grids. Japan already had, as of 1926, a heavy water production plant that could rival Norway's. She had access to uranium. She had the academic talent, too. If you can convince the Japanese government that it's worth the price--worth insane amounts of money, worth less military spending, worth hiring expensive foreign researchers who are probably subversive, even worth cutting off half the nation's electricity for half the day every day to give it to the lab--I think they can get there. Will the Empire of Japan be the first nation to get a bomb? No--but they WILL get one.