The Judge is a little more overstable than the Proxy or Pure, but you could certainly beat one in to cover this role. They feel very different than the Pure or Proxy do though.
I think both the Proxy and Pure are very good discs for this slot.
The biggest difference in flight is the Proxy has rock solid high speed stability no matter how far you throw it. The Pure will start to show a touch of turn past 230-250', and the effect becomes more pronounced as you get further out. Most people don't use putters in this range so this won't matter to them.
Rim feel is also different. The Pure has a flat bottom wing while the Proxy is just barely concave. The Pure also has a more rounded shoulder VS the flatter Proxy. Most people, including me, prefer flatter topped discs for forehand shots. I can't find the specifications for the Proxy height but I'm pretty sure I remember Pures felt just a touch taller. They both have 10mm wings.
The Pure is available in baseline, so there's that. The MVP Atom is pretty close to a baseline Proxy though.
I prefer the Proxy. It does better in the wind, holds truer lines thrown past 200', flicks better and fits my hand better than any other driving putter I've used.
That being said the way I use putters can be different than how a lot of players use them, so maybe the different plastic options mean more to you than how well either disc holds a laser straight line off the tee.
Here's a Proxy refusing to flip to flat, much less turn over, on a 400'+ throw