Having flown both the Orion (P3B and P3C) as well as the Nimrod, I can verify that one or both outboard engines were regularly shut down to improve endurance.
In the case of the Nimrod, the Flight Engineer would calculate 'Crit Weight' before the second Spey was shut down. He would also write the Min Drag Speed on a placard for the pilots, who would ensure that the aircraft was flown with a safe margin above that speed. Should one of the running inboards fail, selection of full power on the remaining engine would guarantee a minimum rate of climb of 200 feet per minute whilst the first outboard was relit.
I have shut down engines in flight on hundreds of occasions and not once was there the slightest problem restarting them.
Is it not ironic that the Nirod was the only Long Range Maritime Patrol aircraft to have an in-flight refuelling capability, which would have been of tremendous value in the present search.