Strafing runs?
With the greater ceiling and speed, you could be on the Zero from above and behind before they even knew you were there (I don't think they had onboard radar lol...) and it would be a lot easier for the 1941-era Americans to produce cannon rounds for the F14 than to try to produce air-to-air missiles w/o the ability to produce integrated circuits, i.e. impossible.
And since you're basically trying to make a 1-pass kill at high closing speed, I don't think you're going to be around long enough for the Zero to try to train its guns on you, fire, and hit anything...
Agree on the air-to-air missiles. In this scenario the inventory on the ship is it, there will be no replacements.
You are right about the cannon rounds. The F14 had a 20MM Cannon and WWII US Industry was obviously capable of producing 20MM Cannon rounds (not the exact same gun nor round but for example the WWII era P38 had a 20MM Cannon as well).
Two things about Strafing runs:
First, I don't think it is as easy as it sounds. I don't know, but the cruising speed of the F14 is probably ~600MPH while a Zero can barely get over 300MPH max and their cruising speed is around 200MPH so the closing speed is going to be ~400MPH and you are shooting at a fairly small target that can move in three dimensions. This is vastly more difficult than strafing a building, train, or tank that is stationary or can only move at relatively low speed on one or two dimensions.
Also remember that you can't walk the aim all the way up to the target. At some point you HAVE to pull away (up, down, left, right, something). If you don't, you'll crash your irreplaceable F14 into either a Zero or the wreckage of a Zero and trading Zeros for F14's is a winning strategy for the Japanese.
Second is something that you would never suspect but I find interesting:
Years ago I read a book about Spitfires that was a compilation of pilot stories arranged chronologically. The last story was by a pilot who was assigned to "play" the enemy in mock combats for the British when they were getting ready to face some rebels who had WWII era planes somewhere in the 1960's. Ie, he was flying a Spitfire as the "Scout Team" so that they could figure out how best to take on WWII fighters with much newer jets.
They started out thinking what you suggested, from above. That makes sense because ever since the first air-to-air combat opposing pilots have always considered altitude to be an advantage. In this scenario, however, they determined that the jet was better off coming in from below because the prop-plane pilot has little or no ability to see something coming from that angle and because the jet had such a massive advantage in power/thrust to weight that altitude was unnecessary. The Jet could come from below, fire, and just keep climbing at an angle that the prop plane simply couldn't follow.
