What you’re looking for are first class existential types:
If Haskell had that, then you could write your desired function as follows:
newtype AnyFn = MkAnyFn (exists a b. (Show a, Show b) /\ Fn a b)
toAnyFns :: [exists a b. (Show a, Show b) /\ Fn a b] -> [AnyFn]
And you might not even need the AnyFn data type at all.
Also, the AnyFn type should be pretty much equivalent to your original AnyFn type that uses ExistentialQuantification, but I saw somewhere in the GHC proposal that these two features are not yet designed to work well together.
