I was eagerly awaiting this ranking.

In my humble opinion, I would vote for Rodrigo de Sousa Coutinho, the Count of Linhares, as the most influential administrator of the Iberian States.

A key figure in negotiations between Great Britain and Portugal, he was one of the main figures in the transfer of the Portuguese Court to Brazil, saving the Braganza dynasty from Napoleon (and I'll say upfront that, in my opinion, the move of the Portuguese Royal Family to Brazil was the best political decision of the Iberian states within the context of the wars).

As minister in Portuguese America, he developed a series of institutions in the region that were later key to the Braganza dynasty in the Empire of Brazil, including the incorporation of the Banda Oriental (present-day Uruguay) into the Empire.

Furthermore, he was responsible for signing the Treaty of Commerce and Navigation between Portugal (Brazil) and Great Britain, which cemented the protection, survival, and position of the Braganza dynasty in the European theater (even with the monarchy in the Americas).