Obviously from your description it *sounds like* you have the same thing going on, but make sure you do double check it’s not something else before you go modifying bits of kit!
I even went as far as taking the headset out of the frame, and then checking where the contact was as I slid the cup (with bearings removed) down onto the steerer as the first time it happened I was convinced it couldn’t be that, but sure enough, contact occurred with the cup still about 1mm from where it should be once bearings and crown race fitted.
Check there’s no burs or other damage to the inner face of the cup that could be contacting as it could be that rather than it being a tolerance thing.
and yes, I filed the headset cup inner edge (with bearings removed!) as it only needed a tiny bit taking off to clear, I wouldn’t file the steerer.