The USAF had a problem with the O-2 in that the rear engine provided considerably more thrust than the front engine, but it was much less obvious when the rear engine quit. They had to add additional alarms to let the pilot knew when the rear engine quit, to prevent him from getting into trouble by doing some maneuvers with the rear engine dead.
The civilian 337 had incidents of pilots taking off on the fwd engine only after either a failure or failing to start it. (The airplane was universally reviled during the '70's and '80's. It seems to have a better reputation today as long as it's serviced by someone who knows the quirks. Especially keeping the aft engine cool.)
The XP-54, XP-55, XP-56 did not inspire the Shiden. No one knew outside the people who worked on them about those American experiments until after the war was over.