Operation Ten-Go had the following order of battle on the side of the IJN:

BB Yamato

CL Yahagi

DD Asashino

DD Hamakaze

DD Suzutsuki

DD Kasumi

DD Isokaze

DD Fuyuzuki

DD Yukikaze

DD Hatsushimo

Over 100 aircraft delegated for ground attack duty (mostly kamikaze)

The Allies had something on the order of 300-400 planes as well as an entire surface task force (that was ultimately unneeded).

Tameichi Hara was the captain of the Yahagi. He was known to be a destroyer and torpedo expert, though, and not a cruiser expert. He speculated he was picked for this position because he had a reputation for being lucky. Similarly, DD Yukikaze was known for being a lucky unsinkable ship (although ships that it was escorting tended to take heavy losses).

In his memoirs, he writes about the sinking of Force Z back in December 1941 by Japanese land-based aircraft. A fleet very similar to this one, BB Prince of Wales, BC Repulse, and 4 destroyers, was sunk by a force of less than 100 planes, and only a few planes were shot down. Simply put, naval antiair was very weak.

In his past career, he had been the captain of an old destroyer, DD Shigure. He had evaded Allied air attack through a few strategems, including a bit where he chose to forsake evasive action for speed. This was because of how anti-aircraft guns fired-namely, they fired as a projectile that goes in a straight line, gradually losing upwards velocity until the shell falls. Typically, destroyers and light cruisers would evade by swerving left and right to make a harder target for planes. Doing so, however, means you travel "slower," and also means your AA guns will have a very hard time shooting down planes.

So that was the reason why the CLs and DDs accounted for so few planes: because they were too busy evading for their guns to have accuracy. Unlike the Americans, the Japanese did not have radar-linked fire control, and their guns were essentially aimed manually. Thus it was hardly surprising that any aircraft hit were entirely due to blind luck.

But what about BB Yamato? Yamato was bristling with AA weaponry, not the least of which were her 46cm main guns, which were equipped with Sanshikidan (Type 3 Shell). These shells would burst in air, spreading inflammatory rounds over a large area. Theoretically, it would be a great area of effect weapon against large swarms of planes. In practice they were pretty ineffective aside from shelling airfields.

You also need to consider how planes attack ships. While torpedo bombers need to approach the ship from its broadside at a level height, rending it extremely vulnerable to aa fire (relatively), dive bombers attack from the bow or stern side. And bombs move forward when they are dropped, but the sheer size of the ship meant that even a misaimed bomb could still hit something.

On top of all this, Yamato was considered, incredibly, a "fast battleship." It had a speed of 27 knots, and it had actually evaded many torpedoes at Leyte Gulf (while its sister, Musashi, failed to do so). It too was trying to evade torpedoes and bombs, in the process making its AA fire inaccurate.

Lastly, and probably most critically, there was no Combat Air Patrol over the ships, as you say. There was simply no way an unescorted surface group could stop that many planes. If a group of one BB, one BC< and 4 DD couldnt stop 90 planes, it was pretty ludicrous to think 1 BB, 1 CL, and 8 DD could stop 400 planes. As Tameichi Hara said, the mission was a pure distraction to allow the kamikaze bombers to go in.

Sources:

Hara, Tameichi, Japanese Destroyer Captain.

Spurr, Russell, A Glorious Way to Die, the Kamikaze Mission of the Battleship Yamato

Mitsuru Yoshida, 戦艦大和 (Senkan Yamato, or Battleship Yamato (please do not confuse this with Space Battleship Yamato)). I actually watched the movie rendition of this, but there is also a book, although I do not believe it is published in English.