Maybe FDR’s “shoot on sight” order would rile up the excitable German dictator enough to commit a serious “mistake” against the US?...................................... Yeah, it would be like an Oil Embargo against Japan. Had Hitler remained cool, Roosevelt would have sent all his resources to the Pacific instead of Europe. In that case the Germans may have forced Russia to the negotiating table and the war in Europe may have ended on the eastern front and leaving Germany with the nuisance of Britain. Without our total commitment Britain would probably agree to peace terms. The Germans weren’t interested in the conquest of Britain, they were looking east. Lots of iffy history here.
I doubt that.
Roosevelt's focus from the beginning was Nazi Germany, so he was not going to be sidetracked into the Pacific while leaving leaving the main problem unattended to.
Today no one knows how FDR might have finessed it, but everything I've read implies that he would sooner, not later, have refocused the US efforts towards Germany, regardless of whether Hitler declared war, or not.
Once the US was in it, we were in it to win it, and Hitler's Germany faced total destruction.