How to get the Datatype Info from a type after SOP representation conversion?

I'm trying to do some shallow printing on datatype names but I'm not sure how to do this with Generics-SOP.

For the cases where I have a List of my newtype, I can print out what I need fairly easily:

class GTypeName f where
  gtypeName :: g f -> String

instance (HasDatatypeInfo a) => GTypeName (SOP I ('[ '[], '[a, [a]] ])) where
  gtypeName _ = "(Array " ++ name ++ ")"
    where
      name = datatypeName $ datatypeInfo (Proxy @ a)

As you can see, I'm matching on the List kind and using the inner a's Datatype Info to get the name out. But I don't know how to handle the case where I want to get the actual top level constructor name itself.

In GHC Generics I did the following:

instance (GTypeName f) => GTypeName (D1 m f) where -- peer inside
  gtypeName _ = gtypeName (Proxy @ f)

-- go into the Cons constructed type
instance {-# OVERLAPPING #-} (GTypeName f) => GTypeName (C1 ('MetaCons ":" g s) f) where
  gtypeName _ = gtypeName (Proxy @ f)

-- return the constructor name here
instance (KnownSymbol n) => GTypeName (C1 ('MetaCons n g s) f) where
  gtypeName _ = symbolVal (Proxy @ n)

-- take the left side, as this is the result of a type product from Cons
instance (GTypeName a) => GTypeName (a :*: b) where
  gtypeName _ =
    gtypeName (Proxy @ a)

-- match on array and take it out here
instance (GTypeName b) => GTypeName ((C1 ('MetaCons "[]" g s) f) :+: b) where
  gtypeName _ = "(Array " ++ gtypeName (Proxy @ b) ++ ")"

This is ultimately used with a newtype and some data types like so:

newtype Status = Status Text

newtype OpenRequest = OpenRequest
  { path :: Path
  }

data Route req res = Route
  { method :: Method
  , url :: Url
  }

open :: Route OpenRequest Success
open = Route {method = POST, url = Url "/api/open"}