Quite sincerely, they should just look into running WebKit server-side.
That said, in my experience if Apple has secretly decided they don't like you, they tend to move the goalposts on you in subsequent reviews, so migrating their systems to WebKit may not be time well spent.
Server-side??? Apple requires apps use the Apple WebKit framework only for web content, which runs only on the client-side. The point of Puffin is to run Flash and other desktop crapware websites that don’t work on Mobile Safari (Apple WebKit) properly.
Puffin isn’t a native or local web browser; it’s an optimized, virtual, remote browser viewer. If they sell it as a “Citrix for the web,” they might have a shot.
That said, in my experience if Apple has secretly decided they don't like you, they tend to move the goalposts on you in subsequent reviews, so migrating their systems to WebKit may not be time well spent.