So, I got some advice from a local planning consultant.
As discussed I am happy to share my initial thoughts on your proposals for the barn.
The location is outside of the Grade II* Registered Park, but visible from it. The change from being an uninhabited farm building to a residence will be resisted by Historic England because of ‘intensification’ of use - lights/cars/garden structures/fencing.
The site is within the theoretical zone of visual influence of the Grade I House, though in reality it may only be visible from the roof of the main house.
No conservation or listed buildings are nearby and the site is within the harbour run-off water zone – not a problem in reality.
The Local Planning Authority will be resistant to development in the open countryside and on sites that are not sustainable, which in this case would be car reliant with no local amenities.
In conclusion the possibilities for residential conversion/re-build are slim. You can seek the formal LPA views by a pre-consulation application (fee of £400), which, as I said, I am happy to assist you with in writing the letter of application.
Hmmm. I'm now on the fence as to whether I throw £400 away or just give up on it.