I might
See here is the thing - I get it Japan is mountainous - but where are the towns cities and industry and the majority of its farm land?
Not in the mountains - the majority is on or near the coastline - the so called Plains and lowlands - where most of the people are - here is the planned landing and initial assault zones for Coronet - you may notice the Green areas where the allies are landing and intending to take and the Pink zones (mountains)which they are not.
Once the majority of the Urban areas and arable land has fallen to the allies (and Im not suggesting that it will be a picknick) the Japanese resistance effectively becomes an insurgency type war with man packed weapons vs the most powerful army's the world has ever seen and ones not constrained by 'Heroic restraint' ie they will use every weapon in the arsenal.
The Wallies had done insurgency before and in this particular case no one is supplying said guerrillas with weapons supplies expertise and political support
At some point between the first Allied landings and the last mountain village consigned to fire the Japanese government will have thrown in the towel - and for the sake of the Japanese peoples I hope that said towel throwing is not long after the first LSTs hit gravel.
Not that simple. The major coastal plains were (Kanto plain and Nagoya) have the waterways flanked by mountainous peninsula within artillery range. Furthermore, the largest plains are actually reclaimed swamp which is easy to turn back to swamp again. Easy to land, difficult to advance, reinforce and supply. Also major population centers do exist in narrow (compared to artillery range) inland valleys which represent a natural choke-points. Just few of these: Kyoto, Nara, Matsumoto, Kofu, Asahikawa and Morioka cities. Actually all these cities held rear bases of Japanese armies in 1945. Some cities even reside in volcanic craters (Aso). Basic Japanese plan was to give up the ~10 km deep coastal area and to whittle down US forces by artillery fire from mountains, while militia forces prevent rapid advance up the said mountains, using choke points to negate US advantage in numbers and firepower. The Allies took 2 years to take majority of Italy, even with easier terrain, less strained logistics and more cooperative local populations. The campaign in Japan may take approximately the same time or even longer before degenerating into guerrilla warfare. Assuming the centralized surrender do not happen, my estimation is 9 to 30 months until Kyoto and Matsumoto cities (the last major industrial centers) could be taken. Time is very sensitive to minor effects like weather or tactical decisions. War for choke-points is very chaotic by definition.
The basic math the Japanese planners of last stage of Pacific war used:
1) The kamikaze were expected to kill 3 US men per Japanese pilot, after corrections for radar shadows from landmass. For "Operation Downfall" about 10,000 kamikaze planes (mostly converted trainers and old recons) were held ready, with 10,000 more to be mustered on the basis of needs. It mean likely the full annihilation of US Navy radar picket destroyers and several capital ships sunk in the day of invasion to Kyushu.
2) Japanese average troops (50% combat rating) defending the hard terrain in full reach of naval bombardment (Palau, Iwo-jima, Okinawa) were capable inflict 1.3 casualties per Japanese soldier killed, with 1/4 if US casualties being KIA. The fighting quality of newly assembled militia divisions was expected to be about 30%, giving 4 KIA Japanese for each KIA American.
3) The unrestricted submarine warfare with huge Japanese operational advantage. Japanese have reserved ALL of Kairyu-class short-range submarines (over 200 vessels) for this stage of war. Expectation was sinking of ~500 US vessels with the loss of 100,000-300,000 American lives before the submarine fleet is destroyed.
4) The maximal amount of troops the US were able to commit due supply constraints so far away was about 6 millions. After additional 1.5 millions US soldiers KIA and ~4 millions WIA (making 5 times the total OTL US WWII loss) and military stalemate in Honshu the sort of peace treaty on better terms was expected to become possible.
Of course, it was the worst possible outcome Japanese were preparing for. The implementation of plan turned out to be unnecessary as the Emperor Hirohito, in light of poor performance of Japanese armies in Manchuria, decided the lowest risk decision would be to accept surrender.