[sigh]
Okay. Thor? Assert less. Ask more questions.
For one, close range is a bad idea. You forgot something important about battleships and battlecruisers: secondary guns. As designed, the Lexingtons had fourteen 6" guns to go with the eight 16" ones. Those have probably been updated and replaced with some kind of 5" or 6" dual purpose gun (giving her nasty long range AA capability). But they can still be fired at ships.
At 30000 yards, Abyssara can throw about sixteen shells a minute. They're big shells, but there's still only sixteen of them- two rounds from each of eight guns. She has radar fire control, but I imagine that Alaska does too. While Abyssara probably has a major advantage in terms of ability to absorb hits, they're at least equally able to score hits. Alaska's armor won't keep out 16" shells, but Abyssara won't be stopping 12" shells either, and Alaska can throw about three salvoes to the Abyssal's two. Twenty-seven rounds per minute, instead of sixteen.
Closer in, the situation turns around.
At no less than 18000 yards, Abyssara can throw, roughly, a hundred shells per minute from the secondary battery. And that's one of the most favorable possible cases- if the 6" secondaries were replaced with 5" dual purpose AA guns. The individual shells won't usually inflict that much harm on a cruiser. Usually. Nevertheless, that is a hundred shells a minute. The Japanese cruisers would be ripped apart. Alaska has enough armor that the secondaries can't penetrate her actual belt or deck protection, but they'll still probably make hash of her superstructure.
If the Abyssal 6" guns were replaced with WWII-vintage 6" guns, the rate of fire drops, probably more like sixty shells per minute. But the effectiveness of the shells goes up, as does their maximum range (roughly 26000 yards).
Basically, battleships designed in the 1920s and earlier had heavy secondary batteries designed precisely to ensure that no cruiser-weight opponent could possibly get within close range where their lighter guns might be effective against the capital ship's armor belt.
...
Meanwhile... Chaff and radar jamming are actually not bad ideas as such, but making it work in the time available is very, very iffy. Chaff is a temporary measure and works best against air search radar. It will not help against a battleship's fire control radars. And planes close enough to Abyssara to interfere with her radar within her gun range will be getting slaughtered by AA fire from her and her escorts. Using the same planes to launch an air attack and hope at least some of the munitions actually hit the target for a change would probably be more effective, if we're looking for ways to expend the pilots' lives in hopes of harming the enemy.