The Japanese had radar. They even had aerial versions. (The Germans as well, and much better). It was more prevalent later in the war. But by that time they had no gas. We had cut the Japense off.
The Japanese used search radars, and played around with fire-control. They figured stuff out on their own, as well as got a little help from the Germans. This effort was augmented by the occasional capture of our stuff.
However, that said, they were true believers in optical gunnery, and arguably were the best in the world at it at the time.
The width of the target has not as much bearing on getting a hit as you think. The rounds are not dropping vertically. They are coming in on a slant (on purpose). You can do high angle, but it is harder to get hits. Most tactics called for adjusting charge and angle for a nice angled entry.
In naval gunnery, the left/right bit is the easy part. It is the up/down that gets you.
The Japanese went so far as to develop special fuses and tactics to hit in front of the Target, and then the rounds would "torpedo" their way into the ship underwater. The Japanese figured that it would increase chances of hits, as well as incident damage due to shock on non-penetrates/non-contacts. The other idea was to get the rounds under the torpedo belt armor to thinner skin. They definitely tried to use this, and interestingly enough at Leyte is casused them problems on two accounts. One was it used an AP round, that round would typically go right through a DD/DE without detonating on a hit. The other, was for DD/DE, when placed properly, and splashing in front of the target Destroyer/Escort, it would also pass under the hull because of the shallow draft. The Japanese suffered many wasted rounds over this.
In regard to Radar, with a little help from the Brits on the front end, we ran with it, and by the end of the war, one could argue we had fielded almost as many radars as we had mounted guns...
A side note, back in the day, I started out as an Electronics Tech and learned tube based surface search Radar. The SPS-10 specifically.
The development of atomic power, though it could confer unimaginable blessings on mankind, is something that is dreaded by the owners of coal mines and oil wells. (Hazlitt)
What I want to do is to look up C. . . . I call him the Forgotten Man. (Sumner)