You know the thing is I don't think this is possible. Whether intended or not B444 has recreated the European alliance blocs as they existed in the early-mid 17th century vis-a-vis France-England and Ottomans-Safavids.
The French and Ottomans IOTL, and the Arletians and Byzantines ITTL, shacked up in the 16th century to counter Austria, specifically in Italy. As a result France/Arlet and Ottomans/Byzantines have had friendly relations despite the distances involved and the differences in culture and religion, moreso prevalent IOTL than ITTL. In the OTL 17th century the British sent men, on the Urging of Shah Abbas the Great and English Adventurer Robert Shirley, to help modernize the Safavid military and bring it up to western standards. The British agreed both to counter the Ottomans, a French ally, and gain a friendly nation in the Indian Ocean they could trade with. Their actions were highly successful, and directly led to the abolition of the Qizilbash and the elevation and expansion of the Janissary-style Gholams as the main military unit of the Safavid Empire. This is extremely similar to what we have ITTL with the Triunes and the Ottomans under Ibrahim. The enemy of my enemy's ally is my friend, was essentially both of their logics.
The realities of world geography create the positive relationships between England and Persia, regardless of timeline, so long as France, Germany-Austria, and an East Mediterranean Empire exist. And they pretty much always do.