After July 1937, Japan may had two narrow windows to try to escape the China quagmire.
The first was too early for your requirement but between 23rd November 1937 and 12th December 1937, Chiang might have been willing to make peace or at least he told the German Ambassador that he was interested (possibly on 2nd December). The logic was that Chiang had hoped that there would be intervention by either the Anglo-Americans or by the USSR but on 23rd November the Nine Power Conference broke up without proposing any action. Chiang's forces had been heavily defeated both around Beijing and Shanghai. His capitol was threatened and he had lost sufficient forces that his power relative to the warlords was reduced. Clearly his position would have been even weaker after he had accepted an unpopular peace but he might have accepted a peace based on status quo ante (with the arguments about what was the status quo ante left for later). At that point, he may not have been totally confident that he could withdraw into Sichuan because that area was held by warlords especially Liu Xiang, who was not a close ally. On 12th December, the Japanese sank the USS Panay and renewed the hope of foreign intervention. Simultaneously, atrocities around Nanking made it much harder for any Chinese leader to make peace. On 20th January, Liu Xiang died (some have suspected poisoned by Chiang's agents) and subsequently Chiang gained control of Sichuan.
The second window occurred within your required period from May/June to September 1940. The effects of the German victories was that the North of French Indochina fell into Japanese control (the USA reacted later to Japanese forces entering Southern Indochina to threaten Malay) and Britain agreed to shut the Burma Road. Meanwhile the USSR was now focused on Germany and was willing to agree a non-aggression pact. Thus none of the powers wanted to be distracted from Germany by Chinese affairs and Japan could have moved forces from Manchuria into China while mobilizing their economy to build tanks and trucks to use in China. Japan could also have built up Wang Ching-wei's Government. Naturally, Chiang again offered negotiations, probably as a device to win time. Amazingly, the Japanese neither launched major offensives in China nor offered generous peace terms (with a strict time limit for acceptance) but instead signed the Tripartite Pact in September 1940 and concentrated on building up their navy for the clash to come (actually spending on the Navy was the Navy's price for agreeing the Tripartite Pact).The British then reopened the Burma Road and the USA moved towards Lend-Lease.