While it was very true that the militarists had a lot of power by this date, I am not so sure that even if the war in China had continued that the US would have declared war...
There was a very huge, very influential, and very vocal China Lobby in the US during this period and FDR was savaged on all sides for his "weak" response to the Panay Incident.
A continuing war in China is going to mean a continuing need for resources by Japan and continuing US material/financial/diplomatic support for the KMT. Sooner or later, Japan is going to need resources then currently in other hands in order to continue her war with China and sooner or later US material/financial/diplomatic support is going to be seen by Japan as a problem which needs to be "rectified".
As long as Japan stays in China, war with the US is a distinct possibility.
That said, perhaps a POD during the incident is needed. Another possible way for the militarists to lose power is if Prince Konoe had acted to curb there power during his time as PM (I'm not that sure that this would work).
If your not sure how a POD would work, you have no POD at all.
All but the most hard-core backed down after the emperor's order...
And they were still covertly protected by factions within the government.
... although it did take time.
Again thanks to the political cover afforded by sympathizers within the government.
The various IJA factions leading Japan to war had powerful patrons within the Japanese government who either agreed with their actions or were happy to advantage of the events created by their actions.
And I would argue that it was a very different faction that responsible for the Marco Polo bridge incident.
Don't fall into the trap of thinking of the factions involved as monolithic or even "led" in some traditional fashion. There were no lodge meetings, secret handshakes, or grand masters at work here.
Instead, you had an every shifting welter of inchoate groupings all fervently believing in a Greater Japan and her imperial destiny while all disagreeing on a few of the details of how to achieve that Greater Japan and destiny.
Think of a centipede whose legs all have their own "brain". Each of the legs is wants the centipede to move towards a distant leaf and each of the legs thinks it alone knows the best way to get there. Sometimes the legs act together and sometimes they'll act individually, but the centipede will eventually get to the leaf in question.
Eventually it will get to the leaf and the foot waiting to smash it.