Need a very simple WW2 Europe conflict resolution

I think that the 'tug-of-war' idea for investments would be a nice simple way to solve the problem, if, as you say, you were able to think of a way to make it advantageous to make consistent smaller investments. Perhaps each investment could be worth a certain number of spaces on the track- 25 might buy 1 space while 2 at once would cost 60? Seems an idea worth pursuing anyways!

Why not simply have a "European front" deck to dictate how much the USA need to invest on that front?

It could work like this:
The deck has cards with values from 10 to 40 (with an average of 25 per card). The deck is shuffled and placed face down to form a reserve. The USA player starts his turn by drawing one card from the deck and placing it face up next to the reserve. This represents the Germans investment on the European front the USA needs to counteract.

Then the USA player allocates resources to the European front, up to a maximum of 50 per turn. If enough resources are allocated to match the value of the face up card(s), the card(s) and the corresponding resources are removed. That might leave some resources unused that will help cover future cards.

If the European fron ever accumulates up to 100, USA loses, or is forced to allocate all its resources to the European front or whatever you find works best for the game.

That will force the USA player to allocate some of its resources to Europe, but also give him some tactic and strategic freedom, and introduce the push-your-luck element you want without making things too complicated.

If the game is about the Pacific, I would say just let the game happen in the Pacific. I would have no problem seeing the entire United States on the map of a game (say, axis and allies Pacific) while knowing that I was only receiving in resources what the U.S.A was able to allocate to that theater historically.

I see issues with giving one side in the game more resources than you ever intend them to be able to bring to bear on the other side. If the United States get's to use extra resources, it sounds like the game would be pretty imbalanced. So, it seems like you're pretty much forcing them to spend resources. So, any choice in the matter is largely an illusion. If there is no random element involved in deciding when and how much they pay, and the European war model is simple, the optimal use of resources should be pretty easy to figure out. Then there really is no choice. In that case, just figure out how much you want them to be using, and give it to them instead.

If there is a random element, we then would have to assume that it will be one that has enough impact to merit using it instead of simply setting up the U.S.A with the desired resources from the start. This brings up the scenario where I just finished a two hour long (or however long this game will take) game to hear my opponent mumble something about having had a better chance at midway if the Germans hadn't been so demanding. At least let him complain about the dice rolls there, so I can comment on training his fighter pilots better, rather than fishing for references to a nation we never even saw in the game.

Either the European front has a prescribed, predictable effect on the game, in which case it should be scrapped as unneeded, or it adds a random element that has nothing to do with what the game sounds like it's actually about which might upset enough people that it should be scrapped.

Again, I'd say don't worry about the European theater in the Pacific game. (If German planes had been attacking Hawaii, this might be different!)

Anyway, here's my idea:

Two tracks, one for the Japanese, one for the U.S.A.

The Japanese advance their track through some means of winning battles, holding territory (the more they do whatever it is, the faster it advances.) This would represent their ambitions to solidify a pacific empire. If the Allies can't stop them in time, the game ends. I believe A&AP has something like this.

The Americans have a track where they do something (Spend resources? Forgo construction? Use up troops? Not attack this turn?) which advances their placement on it. At the end of this track, they have figured out how to build the atom bomb. I think we know what happens if the game gets that far.

Maybe this doesn't fit at all with the theme or the mechanics you plan on using. Maybe it suffers from the same problems I had with the European aspect. It would certainly require the proper balancing, but I suspect some variation of it would feel much less clunky than European influence in a game about the Pacific.