The 60hz radiation picked up by the bridge single coil would still be present, because there would not be a RWRP coil to cancel the noise.
You can achieve the sound you want by putting the bridge humbucker coils in parallel, then putting that signal in parallel with the series neck humbucker.
101: Any two single coil pickups of opposing magnetic polarity and wind direction will be hum-cancelling when combined in either series or parallel operation.
If you combine split humbuckers and find they’re out of phase, either swap the humbucker start and series-connection leads that are grounded when split to select the other coil, or reverse the wind of the desired coil by swapping the start and finish wires. This will entail rewiring the order of the two pairs of start and finish wires of the humbucker, in order to preserve both humcancelling and (potentially) its in-phase relationship with the other humbucker.
If they’re in-phase but producing 60-cycle hum, then flip the magnet of one pickup.
This strategy can be used to ensure that any desired combination of north or south coils between two pickups is humcancelling - It will only ever involve the changing of magnetic polarity and/or reversing the wind of the pickup via the start and finish wires, until you have the result you want.
This is why another theoretical solution would be an additional switch to add a humcancelling dummy coil between the split bridge humbucker and selector switch’s signal path.