QRH,
My memory may have lapsed, duty time regulations are as per your Ops Manual and may vary from other Ops Manuals, and you are complicating your explanation somewhat.
An FDP commences at the report time of 1430, you say 11:30 is allowable thus, normally, you would be out of hours at 0200, check your Ops Manual but normal interpretation is that an FDP ends upon your final 'on blocks', any duty after final on blocks is 'duty period' but not 'flying duty period'.
By this you, your operator, needs to find an extra 1:15 from somewhere thus you need the minimum split duty of a 3 hour break, it seems you achieve this with a 3:15 hour break.
A split duty is an extension of duty however it is not 'commanders discretion' but what I cannot recall is if a commander is permitted to exercise discretion to (further) extend on a split duty FDP, I've a feeling that he/she cannot.