Battery Power Supply Yes_ or No_

Power is just one of many ways noise has of getting in there. A battery is one way of lowering noise. My motor was at one point upgraded with battery power. It does make a difference. Even with the battery though it still needs to be disconnected from power or noise still comes in. Even then the power supply is but one small part of many. Everything matters. Focus on the battery if you must, but you'll be way ahead of the game if you put a lot more focus on the sound that comes out than the parts along the way. Only once you select the best phono stage that way, then you can look at tweaking different aspects of it. 

In other words buy the Project if you like it the way it is, but not because you think you're gonna make it so much better by replacing a wall wart with a battery. You will make it better all right. But not much. Not much at all.

I can share my experience with battery powering gear. With my CD player, a battery certainly lowered the noise floor but at the cost of decreased dynamics. This is most likely attributed to the battery being too small, not enough capacitance. A linear power supply works better here, at least until I get a larger, better battery. With my tube preamp buffer, it sounds much better on the same battery that wasn’t “good enough” for my CD player. It sounds better on that battery than the same linear power supply that makes my CD player sound best. Trying to relate this to your situation, the tube buffer is closer in function to the phono preamp than the phono preamp is to the CD player. The phono preamp isn’t the source, it’s a type of signal amplification just like my tube buffer (which by the way applies 9 dB of gain). I say give it a shot, if you know what you’re doing so you don’t accidentally fry a component, and see how it sounds. From experience and from what others have said, bigger batteries sound better in terms of dynamics. We’re talking 70 Ah or more. Yes, that’s like a car battery in size. Your mileage may vary and you may not need that much. I’m using 35 Ah for my tube preamp and it sounds great. The CD player obviously needs more. 

Why not hang a big cap across the battery? 

noromance.... what is the benefit of strapping a big cap do.  Please advise the logic or benefit of doing this?