score:2
These 2 points should help clarify that it was your #3, a "creeping takeover": The Marco Polo Bridge Incident and China's appeal to the League of Nations in 1938 (pdf) - page 17 onwards. In any case, there was this question -- which is quite close to your current question.
I believe this topic, unfortunately, could be inflammatory for some (as these incidents are of fairly recent past). So, I would leave it at that.
Upvote:2
There is a strategic vision for the Japanese behaviour in China. This strategic reason is based on a few political/ideological reasons:
This strategy consisted in capturing the coast of China: thus, China would lost its capacity to get hardware from other countries and would be more vulnerable. Japan want to control large portions of China: for that it uses regular offensives to capture territories, especially cities and agricultural lands.
During the years 1937 to 1941, Japan achieved a lot of conquests, but the opposition from Chinese was strong enough to avoid collapse: the nationalist governement, from Tchoung Qing, still controlled an army and a state with which it could hamper the Japanese occupation of the coast.
Then, you should consider how the Japanese war went worldwide: to summarize, the blocus of USA about oil triggered a big war in Pacific. With that, Japanese had a little less logistical and air power to put in the balance in China. Still, with what it was left with in China, Japan could launch medium offensive to capture agriculture: this was the "rice offensives", and it could capture airstrips from which the Flying Tigers and Doolittle airplanes operated. On a map, this could look like little conquests compared to China's superficy, but considering ground difficulties and Chinese opposition (which was not zero), this was still good conquests.
To conclude: In the later stages of WWII, Japan was still conquering pieces of land for three objectives:
Japanese land army was still able to perform well against Chinese soldiers or partisans. But a lot of soldiers were needed to hold the territories and defeat those soldiers and partisans: So Japan was stuck in China as much as Chinese forces were stuck in resisting to Japanese movements without offensive opportunities.
Side note: this perfect stalemate was a good thing for the Allies, who had to face Japanese land forces in Burma (helped as well with Chinese soldiers). However, on air and naval battlefields, China did not hamper Japanese capacities and the Allies defeated by themselves Japanese forces.