I don't know how the arrow syntax works, but you can get banana brackets for applicatives with a preprocessor
—the Strathclyde Haskell Enhancement (SHE)[1]. You can install it from cabal and enable it with {-# OPTIONS _GHC -F -pgmF she #-} after which it just works (including, if I recall correctly, ghci).
Personally, playing around with it convinced me that banana brackets aren't quite as nice in practice as they look. They still make *certain* expressions nicer (especially simple ones involving operators), but either don't make a difference or actually make the code *less* readable in more complicated cases. Of course, those more complicated cases end up being the most common, so in a small project I only found something like two applicative expressions where it helped (out of at least 20).
A particular problem I had is that, by necessity, $ works differently inside banana brackets than normally. This is the only thing that makes sense, of course, but it doesn't jell well with how I intuitively use $ as more or less syntax for limiting nested parentheses.
I don't want to discourage you too much. They might work better for you than they did for me. But you should definitely play around with them, preferably on a real project, before you sink any time in trying to implement them in GHC. You might like them but don't be surprised if you don't.
Also, they'd be somewhat redundant with ApplicativeDo. The syntax is different enough that both can be useful, but it's something to keep in mind. At the very least, the ApplicativeDo extension is a good place to start looking to understand how to desugar to applicative operators in GHC.