What do you predict would be the most losses allied navies would take during an invasion of Japan? And how long would it take to take the capital?
Naval losses could be severe. The Japanese had 12,000+ aircraft for use as kamikazes, and they had a decent plan to use them to draw off U.S. fighter cover so the relatively low number of remaining experienced air crew could make conventional attacks.
At a guess, at least 60 ships sunk, 20-25 DD, 20 transports, 20 or more LST (wouldn't be a serious surprise if a couple of CV/CVL and/or CA/CL were lost), 400+ damaged. If the Japanese plans worked perfectly, total ship losses could come close to 100, mostly transports and LST, if the Allied countermeasures worked perfectly, figure 30 ship sunk. Perfect just flat doesn't happen so...
By Capital you mean Tokyo? Late Fall 1946, maybe as late as early Spring 1947. The Kyushu landings were going to be delayed, a typhoon came through the anchorages for half the planned invasion force in mid October of 1945 and was throwing transports completely out of the water and sank, grounded, or damaged around 300 ships/craft/boats.
https://www.history.navy.mil/resear...acific-typhoon-october-1945.html#anchor593215
It would have been early February before the Allies could have landed on Kyushu, considering storm season, other weather, and hours of daylight. That alone pushed the Honshu landing back to August/September 1946.
That whole time ~100,000 civilians a month are dying in areas under Japanese occupation. 20-40,000 Japanese civilians are dying every month from bombing and famine caused by the blockade.
Nightmare all the way around.