Generally sound analysis -- BUT. Washington was "unanimous" in the sense that every elector gave him a vote. Pre-12th amendment, each elector had TWO votes. Each give Washington one of his two, and the other vote was scattered among 10 people, with Adams being elected Vice-Pres by having the second most votes. (This system is what led to the fiasco of 1800, where Jefferson and his putative Veep, Burr, tied by having the same number of votes, as ALL of their elctors voted for both, TJ having forgotten the system and not arranging to have one of his guys drop Burr!)
Pre-12th amendment, each elector had TWO votes.