I agree with your overall analysis, but disagree with some of your math.
America starts with 42 IPCs to Japan’s 30 IPCs. Japan should usually start turn 1 with only one surviving transport, which means Japan cannot really afford to go on any crazy adventures – an aggressive J1 might pick up $1 from Russia, $3 from China, and $1 from Burma, for $35, compared to $39 for the USA.
On J2, Japan could pick up another $2 from Russia, another $1 from China, retake Burma, and maybe pick up $1 or at most $2 from Alaska, Hawaii, or Australia. So even at the end of J2, Japan’s income is capped at $40, much of which needs to be spent on the Asian mainland. Meanwhile, the US will still be earning $38. So it’s not literally true that Japan is out-earning the US after turn 1, and even after turn 2, Japan can’t afford to outspend the US on its navy.
Similarly, Britain starts with 31 IPCs. They may or may not lose Egypt before their turn starts, but they can often retake it, and/or take Norway or NW Europe. So Britain should usually still be collecting $31 at the end of its first turn. They can often repeat this on the second turn, i.e., retake Egypt / Burma or capture Norway or NW Europe. So Britain’s income might eventually go down to $28 or lower, but not at the end of the first turn. It’s also not fair to compare Britain’s income directly to Germany’s, because Germany is also fighting Russia, especially in the early turns when Russia doesn’t really have to spend any money/troops against Japan. Russia should be earning at least $26 in the first few turns. Assume that the UK max-places infantry in India every turn, which costs $9. So, the combined UK + USSR income of $28 - $9 + $26 = $45, which is about the same as Germany for the first few turns. Germany starts with $41, and they will often lose West Russia and trade Leningrad and Stalingrad, which puts them up $4, for $45. So there’s economic parity on the western front, to start with.
And this is exactly the problem: as you point out, the Axis have economic parity in Europe after one turn, and in the Pacific after two turns. The Allies, at most, will earn a premium of $15 over the Axis before the Axis can eliminate the Allied economic advantage, and that money isn’t nearly enough to build the fleets they need to cross the oceans, let alone to establish a viable beachhead. The Allies don’t have an opportunity to set up a meaningful advantage anywhere on the board before the Axis start double-teaming Russia. This is not just unbalanced, but boring: the most interesting positions arise when each side has (at least one) advantage, and you have to win the game by exploiting your advantage and neutralizing your opponents’ advantage(s). 1942.2 doesn’t generate those positions very often because the Axis are the only ones with any structural advantages. The Allies have to rely on either bad Axis dice, a large bid, or a bad Axis mistake in order to establish any counter-play. If the Axis play a perfect game and don’t get diced, then the Axis will win every time, no matter what the Allies do. This is probably true even in 1942.3. I haven’t playtested it, so I can’t be sure, but I don’t see anything in the 1942.3 setup that would alter the fundamental strategy. As you point out, DespotDoug, the problem is with the income values on the map at least as much as with the particular setup of the pieces. To fix the scenario by tinkering with the pieces, you would need to give the Allies either a fleet that can survive the turn-1 Axis airblitz, or an offensive striking force somewhere in the British south, or both.
If you wanted to try to fix the problem by fixing the income values, I favor adding +1 IPC each to West Canada, East Canada, Australia, South Africa, Persia, Alaska, Hawaii, Sinkiang, Archangel, Vologda, Evenki, and Novosibirsk. I won’t say more than that here because it belongs on the House Rules forum, but feel free to post in House Rules, or to PM me, and I’ll be happy to discuss it further with you.