The version you want to fall back to has been removed from the steam depot as well as from factorio.com, so unless a developer loads it back in you will not be able to fall back. Unless they specifically suppress any changes to the factorio installation all the other players on the server will be ...

I do not have desired answer for you, but why not to update server?
I'm thinking that'll be my best bet and I've already poked the guy running the server, I just don't expect him to be able to do anything about it the next couple days. I figured if there was a way I could revert back to 0.16.25 ...

Me and some friends have had a server running on the 0.16.25 beta, though yesterday I downloaded the 0.16.35 beta to run a local game and see what all was new between that version and the one I was on. I don't really follow factorio news, so I had no clue that I'd wake up to find 0.16.36 be the ...