If it were me, I would advise Bittersteel to either rotate the capital between the Three Daughters or to build a new city in the middle of the Disputed Lands at the exact equidistant spot.
In terms of why he didn’t try to conquer the Disputed Lands, Bittersteel was a man with his eyes on the prize and the last thing he wanted was for his fellow Blackfyre loyalists to get distracted with Essos instead of getting ready to invade Westeros.