Contacts with Russia were limited (there's a reason one of the founders of the Muscovy Company froze to death trapped in sea ice), whereas by Elizabeth's coronation, Protestantism is established not just in Germany and Switzerland, but Scandinavia, and seemed to be a serious threat in France, Scotland and the Low Countries, among other places. That's much better in terms of potential alliance fodder than Muscovy, which would be unable to ever feasibly provide military assistance.
Besides, Protestantism had a preexisting base of support. There were plenty of Protestants and Protestant sympathizers running around. That's critical for a religious conversion. On the other hand, Eastern Orthodoxy would have to be imported, with a whole new set of priests and liturgy created. It would be strictly artificial, and imposed from above.