Then again, German submarine warfare made US neutrality impossible.
Actually, no. The Zimmerman Telegram made U.S. neutrality impossible. Submarine warfare was certainly a provocation, but Wilson could easily have (as he did on other occasions during the war) chosen to take the "America is too proud to fight" line and not asked for a declaration of war. He was in his second term of office, he did not plan to run for a third term, he had absolutely nothing to lose politically. What he might have done is what FDR did in the months prior to the US entry into WWII, which is to order US Navy vessels to attack German submarines which are threatening sea lanes used by U.S. merchant ships, without declaring war. This would have addressed the immediate problem of German sinkings of U.S. ships without forcing him to violate his pledge to the American people to "keep them out of war."
The Zimmerman Telegram, however, was a plan for a direct assault on the United States itself. Once that was intercepted and turned over to the U.S. government, and verified to be true, there was no way Wilson could ignore it. He had to ask for a Declaration of War. And he did.