Everything is permitted. First of all, it is likely there was 60x the spoon in the content of the pot. Even if there was not 60x the entire spoon, this spoon presumably became fleishig from a soup or cholent etc, where only a small percent of the mixture was actually meat. Therefore, if say 10% of the soup or cholent was meat and the total volume of the spoon is 20 ml, we only need 60x 10% of the 20ml to render it Batel.
Additionally, there are numerous Sefeikos. If the fleishig spoon was inserted into the Eino ben Yomo pot, certainly the spoon and contents remain Mutar. Even if it was placed in the Ben Yomo, the Mechaber 95:2 and 3 considers this a permissible Nat bar Nat. even the Rema who is Machmir merely cites the Minhag to do so and does not dismiss the Mechaber's position. Furthermore, even the Rishonim who are Machmir presumably only do so miD'Rabannan. Consequently, they doubt regarding which pot the spoon was inserted into is not worse than a Safek d'Rabannan, and we will not forbid the pots either.