Progress in the search:
Progress report 1: Doing some preliminary research, I have come across some interesting links. The most important one is the Wikipedia page for the Bank of the Holy Spirit :
http://en.wikipedia.org/wiki/Bank_of_the_Holy_Spirit. The most interesting part is where it states "In 1786, the bank became one of the first to issue paper money during the pontificate of Pope Pius VI". This document is dated on 1786 as well.
Progress report 2: Some more digging. Found the exact item (or at least as close as you get) MINUS THE SEAL between the signatures on ebay. All of the other ones on ebay are missing the seal as well, but some sold for $130-240. The condition of this item is worse than the ones that have sold, though. It goes to show that the price will be what the seal adds, compared to what is detracted due to condition.
http://www.ebay.com/itm/CEDOLA-18-SCUDI-BANCO-DI-SANTO-SPIRITO-DI-ROMA-12-01-1786-/170977184275Progress report 3: After looking through 30 listings, not a single one had a seal on it.
Progress report 4: I have found a picture of one of these with the seal on it. There is no price attached, but it is from a currency collector's website. It states "7 scudo bank note of the Papal State's bank Sacro Monte della Pieta' di Roma dated 15 January 1788.
This note is of particular interest as it bears an orange hand-stamp of the Papal Legation in the town of
Pesaro.".
http://www.thecurrencycollector.com/pdfs/Italian_Paper_Money_Prior_to_Unification_-_Part_I.pdf