I used to live somewhere where every autumn an interfaith group would organize a really beautiful memorial service for everyone who'd died in the county, but whose body hadn't been claimed by family or friends. Often all we knew was the names; sometimes not even that.

The service would have speakers from various religions and philosophies, but generally, they followed one of two paths. Most people tried to give speeches or say prayers that didn't exclude anyone; like they'd speak of "love" or "what connects us" or something like that, divinity only in the broadest and most abstract terms. Every year a minority of the speakers would just straight up say prayers from their own traditions, but they'd explain the context and what they meant and their personal relationship to the prayer, like they were inviting the attendees to peek into their tradition through a window.

I personally found the second type of interfaith contribution more meaningful and interesting, and it sounds like you would have too, but I assume from the fact that those interactions were always in the minority at the memorial that most people would actually prefer prayers addressed to What Connects Us.