First off, "evangelisch" is tricky for several reasons: it is NOT "evangelical" in the sense most English speakers would be familiar with, it's not merely "Lutheran", and it's not "Protestant", as it includes only some of the older groups like Lutheran and Reformed, but not Baptist, Methodist, etc. "Evangelic" is a word, but it's pretty technical. In any event, "church service" is fine, since in American English at least, I think we'd assume "service" is Protestant (a Catholic service would most likely be called "mass", even by non-Catholics).
That said, the real issue here was how to deal with "verbindender Geist", which I translated as "sense of communion", since this has the added benefit of referencing the church service itself. It sounds "church-ish".
Also, is "genossen" really "enjoyed" here, or is it something else?