In Midway, how do I manage the "inferior" Japanese fleet on day 1?
The other answer got me to look up the game again, and here's what I found.

If the Japanese player is worried about the balance of power on Day 1, he should stay out of the range of planes based on Midway (about half of those of an American carrier, although Midway has a greater CAPACITY than any carrier). This means the normal 7-square "round trip" range, and even the 14-square "suicide bomber" range (the rules provide that if some of an attacker's planes are making suicide attacks, and he suffers combat losses, he can count those losses against the "suicide" planes first).

For the Japanese players, that means staying in columns "A" and "B" near the western edge of the board on Day 1, close to Day 2 reinforcements. If the Americans want to attack beyond the range of Midway based planes, they will do so at a disadvantage. This is particularly true in the advanced game, where Midway would have to send additional fighters to bring the American carrier groups to parity with the Japanese, meaning that the carriers would have room for fewer dive bombers.

On the other hand, the Japanese player may want to seek aerial combat on almost even terms on Day 1, in order clear the way for later waves. With their (future) edge in ships, "attrition," provided that it is balanced, favors them. On Day 1, they enjoy "draw odds," that is if they "draw" on the first day, their reinforcements make them likely to win. 

On Day 2, the focus of the game changes with the arrival of the Atago, a cruiser whose importance is as the flagship of the transport fleet bound for the invasion of Midway. (The way to attack the transports is to attack the Atago.) The Americans can try to prevent the invasion of Midway by sinking the Atago. or follow the historically-based strategy of sinking the Japanese carriers, but they might not be able to do both.

One way for the Japanese to win is to "take out" enough American air power on the first day so the Americans can't prevent the invasion from the Atago. The other, safer way, is to concentrate forces on Day 2 in order to maximize the chances of a successful retaliation against a "first strike."