The challenge with a POD after James II's conversion to Catholicism and ascension is to...
Make it so that by modern times there is a tradition of openly bribing people in the House of Commons to pass agenda. And this open bribery is considered acceptable, and accepting a bribe for choosing policy X is treated no differently or only slightly less acceptable than an MP who supports policy X... after his election.
Bonus points if TTL Pound is worth as much or more than OTL pound and TTL British (or English plus Irish plus Scottish plus crown colonies if there is no Britain) GDP is triple or more than triple OTL counterpart.
Yes, the world discovering new technologies faster (like 30 year early solid state electronics), making the world richer, which means there is more room for a wealth Britain counts too. It doesn't have to be at the expense of the rest of the world. Try to meet the primary challenge at least.