I’m not entirely sure the Japanese could have taken Midway even if they had sunk the three US carriers and lost none of their own.
The Japanese invasion plan was to land some 5000 troops from the Army and the Navy without specialized landing equipment and without any real naval gunfire support doctrine. The troops were primarily armed with rifles, light mortars, and medium machine guns. There was no reserve.
There is no evidence that these troops had practiced large scale operations together, much less rehearsed the landing. Specialized landing craft like the later American DUKW and tracked landing vehicles were never developed by the Japanese. I can’t imagine that the Japanese had even dreamed of them by this point in the war.
The American forces were about 3600 Marines and other support personnel who were well dug-in. They had a platoon of A3 Stuart tanks in support. Heavy weapons included five 5" guns, four 3" guns, twelve 3" AA guns, forty-eight .50 cal guns, thirty-six .30 cal guns. There was an AA unit attached as well with another dozen or so weapons of 3", 37mm, and 20mm size.
Midway is surrounded by a coral reef through which one boat channel, covered by the heavy guns, had been blasted. The Japanese plan was to use their daihatsu barges to land troops on the reef instead of forcing the channel. From there the troops would have to wade about 200 yards through waters ranging from ankle to chest deep to reach the beach.
I am not sure that any Japanese soldier would have survived to make it to the beach. Wading through 200 yards of water ranging from ankle to chest deep or so? The lagoon would have flowed red with blood.
As for actually holding Midway, or even sticking around long enough to blockade it, OttoDaFE is right on the money for the difficulties the main IJN force would have faced.
Without a reserve, there was no way a second landing could be attempted. Despite the damage done to the their air wings, Task Force 16 (Hornet and Enterprise) still had plenty of dive bombers that had proven against Mikuma and Mogami that they were quite capable of wrecking capital ships.
The only way Yamamoto might have salvaged the situation might have been if Spruance, rather than retiring east overnight, had continued west and run into the remnants of Nagumo’s forces in the dark. Spruance, of course, understood that calculated risk did not include a night battle and rightly kept his distance. With that, Yamamoto had no choice but to withdraw.