We will try to understand the cases through thoses described in Gemara. we will examine the similarities and the dissimilarities. The OP says:
They were left in such a way that they seemed to be Hefker.
I even overheard a few people saying "I guess these are the leftover Esrogim and the guy selling them left them for anyone to take".
In Baba Metsia the Mishna said:
מצא פירות מפוזרין מעות מפוזרות... הרי אלו שלו
If he found scattered fruits (on the ground) they belong to him.
א''ר עוקבא בר חמא במכנשתא דבי דרי עסקינן קב בארבע אמות דנפיש טרחייהו לא טרח איניש ולא הדר אתי ושקיל להו אפקורי מפקר להו
There are fruits abandoned on the spot. The owners is not going to bother to pick them up. Gemara discussed for the value, quantity, size and concentration of fruits. The purpose is to evaluate if the effort is worthwhile. If it is the case, the owner will come back.
We have a goods, it can be grain (generally when the mishna says "perot", this is wheat), of any kind of good. The circumstances suggests that a small amount of the goods was abandoned.
Here, in our case the owners were aware that some esrogs had been left behind. But despite this, they did not consider it necessary to cime and collect them. The place is not a secure place. Thus, the owner left them intentionally and this is called "Aveda midaat" (an intentional loss) as one who junk a seal in a non secure place. By their behavior, they showed that they intentionally abandoned them. They cannot come after the Holiday and expect payment. Maximum they can take the esrogs if they are still here. But until ehey get them back, they are not considered their property. Why a synagogue is not a secure place? This is a public place and non-Jewish persons often are cleaning up the spill. Children can damage the Esrogim. and to leave even not intentionally a valuable object in such a place maybe automatically considered as Yeush (they refused to recover them). Gemara told about Bate Knesiot and Makom Sheakum Metsuyim.
Thus we have strong reasons to validate the mitsva without paying.
See SA CM 260, 7. and 261, 4