That map is too implausible. Japan had no hope of actually conquering all that territory or being able to fully subdue China.
For Japan to to not end up "losing" by 1945 you have to solve the root of their problem: China. By 1932, a total war between the two nations was inevitable, because Japan had conquered Manchuria and thus got a confidence boost to its already-powerful pro-war factions. So getting the Japanese to change what they do is out of the question if we take 1932 as the earliest PoD. So we have to look to the Chinese to change something.
In 1936, the CCP and GMD were in a civil war that was only cancelled when Zhang Xueliang, a subordinate of Chiang Kai-shek, had him arrested and forced him to agree to a cease-fire (the Xi'an incident). This showed that the GMD was unstable in leadership and for the Japanese, it also presented the image of a united China arraying against their expansion, so they attacked in 1937.
We need to change the outcome of the CCP/GMD conflict.
So what we can do is have the CCP be crippled, instead of running away to Shaanxi. Mao can be killed by either the GMD or as a result of internal struggle, which will result in a sharp decrease in the unity of the CCP later on. At the same time, we need Zhang Xueliang and others to decide that the CCP is either too weak to be a major threat or to think that they have defeated them, which will prevent the Xi'an incident from happening.
The lack of such a shock could very well delay the Japanese invasion by a year or more, and the GMD could use this time to truly defeat the Communists, or in lieu of Mao's diehard mindset, co-opt their remaining elements. When the Japanese do finally attack, Chiang Kai-shek will be in better shape to engage them, and if he is able to use his extra German-style divisions to dish out some pain in North China, it may be what the Japanese need to eventually realize "hey this isn't working, we should stop". But this won't happen at the very beginning.
The war can drag on for some time, with the Japanese unable to get much headway into China, but simultaneously with the Chinese unable to get anything back that the Japanese have taken. The USA, taking an isolationist stance, does not embargo Japan (allowing it to purchase oil) until late in the war, by which time the front lines have stabilized.
By 1943-45 the Japanese have finally been embargoed from US exports, and are debating what to do next. Some want to carry out a Pearl-Harbor style assault, but rational voices dissent, pointing out that the USN has grown massively in power since the 1930s and that Japan is already war-weary. At the same time, a massive, Verdun-style battle erupts in China, with casualties in the six digits. This kills the hopes of the pro-war faction, and peace talks are entered with the similarly-exhausted GMD.
After negotiations, the Japanese finally agree to leave China proper, but they stay in Manchuria (which the GMD figures it can get back at a later date), Taiwan, and Hainan. By this point, the war in Europe is over, with the Soviet and Americans beginning the Cold War. Japan is bankrupt, and after some political strife the nation aligns with the USA, which makes the same judgement as OTL Germany that Japan is a more valuable ally than China (at least as long as it is supplied with oil). China eventually falls into the leftist camp, having been supplied by the USSR during the war. Japan remains its no. 1 enemy for the foreseeable future.
For Japan to to not end up "losing" by 1945 you have to solve the root of their problem: China. By 1932, a total war between the two nations was inevitable, because Japan had conquered Manchuria and thus got a confidence boost to its already-powerful pro-war factions. So getting the Japanese to change what they do is out of the question if we take 1932 as the earliest PoD. So we have to look to the Chinese to change something.
In 1936, the CCP and GMD were in a civil war that was only cancelled when Zhang Xueliang, a subordinate of Chiang Kai-shek, had him arrested and forced him to agree to a cease-fire (the Xi'an incident). This showed that the GMD was unstable in leadership and for the Japanese, it also presented the image of a united China arraying against their expansion, so they attacked in 1937.
We need to change the outcome of the CCP/GMD conflict.
So what we can do is have the CCP be crippled, instead of running away to Shaanxi. Mao can be killed by either the GMD or as a result of internal struggle, which will result in a sharp decrease in the unity of the CCP later on. At the same time, we need Zhang Xueliang and others to decide that the CCP is either too weak to be a major threat or to think that they have defeated them, which will prevent the Xi'an incident from happening.
The lack of such a shock could very well delay the Japanese invasion by a year or more, and the GMD could use this time to truly defeat the Communists, or in lieu of Mao's diehard mindset, co-opt their remaining elements. When the Japanese do finally attack, Chiang Kai-shek will be in better shape to engage them, and if he is able to use his extra German-style divisions to dish out some pain in North China, it may be what the Japanese need to eventually realize "hey this isn't working, we should stop". But this won't happen at the very beginning.
The war can drag on for some time, with the Japanese unable to get much headway into China, but simultaneously with the Chinese unable to get anything back that the Japanese have taken. The USA, taking an isolationist stance, does not embargo Japan (allowing it to purchase oil) until late in the war, by which time the front lines have stabilized.
By 1943-45 the Japanese have finally been embargoed from US exports, and are debating what to do next. Some want to carry out a Pearl-Harbor style assault, but rational voices dissent, pointing out that the USN has grown massively in power since the 1930s and that Japan is already war-weary. At the same time, a massive, Verdun-style battle erupts in China, with casualties in the six digits. This kills the hopes of the pro-war faction, and peace talks are entered with the similarly-exhausted GMD.
After negotiations, the Japanese finally agree to leave China proper, but they stay in Manchuria (which the GMD figures it can get back at a later date), Taiwan, and Hainan. By this point, the war in Europe is over, with the Soviet and Americans beginning the Cold War. Japan is bankrupt, and after some political strife the nation aligns with the USA, which makes the same judgement as OTL Germany that Japan is a more valuable ally than China (at least as long as it is supplied with oil). China eventually falls into the leftist camp, having been supplied by the USSR during the war. Japan remains its no. 1 enemy for the foreseeable future.