This is a complicated question; it is further complicated by the fact that while agility is important, it's not the only thing you need to worry about on planes.
If you are actually going to build carrier fighters and put them on carriers, then those planes should have the agility designer. Range doesn't really matter when carrier fighters are participating in a naval battle. I'm not talking about fighters on air superiority, but fighters on a carrier running no mission so they can support the carrier in naval battle.
But that is not the only thing Japan needs, as you point out.
There's a lot of air space to cover in the Pacific, and the Zero just isn't going to cut it from land bases in most cases. Take it from someone who shot down around 1000 Zeroes operating from land bases in my last MP game as the US: even with boosted range, the Zero is going to have difficulty getting enough mission efficiency to be useful from land bases. And if the mission efficiency of the Zero is hovering around 30% in a particular air region, all the agility in the world isn't going to compensate for that.
I'm actually a bigger fan of using heavy fighters with the range designer. With a 1940 heavy fighter and the range designer, you can easily get 100% mission efficiency in various air regions around the Pacific (particularly if you boost range as high as it can go via XP). Of course, that means making trade offs to get that plan into action, and you can't fly it from carriers, so... you're back at square one.
But consider this carefully if you like battleships: land based air on air superiority can shut down enemy carrier air power. Thus, with enough mission efficiency and planes flying from land, you don't need carriers at all. Then you can let TACs and range-boosted heavy fighters cover your BBs and SHBBs in naval combat. (Or just bomb the enemy fleets to death if you can't force an engagement.)