I flew the -744 with the P&W4056 engine and had cause to shut one down half way back across the Pacific, SFO to HKG. It was because we were getting a fuel flow filter warning light. The only time I remember windmilling could become a possible problem was if the shut down was caused by loss of oil pressure and/or quantity leading to a windmilling engine without sufficient lubrication.
To get rid of unwanted maintenance messages on the -400 after it had been left unpowered for a while in a humid climate I followed a Boeing engineers advice and selected Alternate Flap switch to 'Alternate' for a few seconds then back to off, messages gone!