So if you have a Mexican standoff in the Pacific, that means you’re both building defensively-oriented navies, i.e., lots of carriers, fighters, and destroyers. It also means you’re both spending similar amounts on your navies. Otherwise, it would be in somebody’s interest to attack.
So, if you don’t want a Mexican standoff, you have to change at least one of those two factors. Let’s say you’re playing America, and you’re at war. You can spend 100% of your income on navy. After about 3 turns, Japan will no longer be able to keep up with you, and will have to retreat. Or, you can spend only 20% of your income on navy. Japan will be able to slowly make progress east across the Pacific, but now you have big money to spend in Europe. Either way, no standoff.
Or, you can build an offensive navy: build mostly subs and bombers. You can force Japan to either retreat or send out lots of destroyers to ‘screen’ you from attacking their main fleet. So instead of sitting and staring at each other, you’ll be trading subs for destroyers every turn, and maybe even getting creative with some can-openers.
Same thing with Japan: if you don’t want a standoff, either spend less on your navy, or have Germany/Italy do something in Europe that will force America to spend less on its navy, or build an offensive navy that’s designed to attack and win instead of just for holding steady in a sea zone.
Balanced Mod creates a few additional opportunities for breaking the stalemate because the NOs give you more islands and sea zones to fight over. Japan wants to take Wake Island and Fiji, the US wants to take back Guam, Britain wants to keep Japanese subs out of the Indian Ocean, Australia really needs to hold the Solomon Islands … so there is more going on in the Pacific, and that makes a perfect stalemate less likely. If nothing else, you need to spread your navy across more sea zones to maximize your income, which increases the odds that there will be a favorable attack to make in at least one of those sea zones.