Phono preamp suggestions

Currently using Moon LP 3 pre with a Soundsmith Carmen 2 cartridge wondering if there is any pre used or new under $600 that would dramatically improve my sound. Using Pass XP10 pre and 250.8 amp.
Not for under $600. You might find a used ARC PH3-SE for a little more that would fit the bill.

But my preferred approach has always been a little different. Rather than shop for a component that fits my budget I try and shop for the components that are serious out-performers in terms of value. Then if they fall in my budget I buy them. If they don't then I put that money to use elsewhere. Done repeatedly over the years it results in a system that punches far beyond its class.

Like right now, $600, hard to say how much more it will get you in a phono stage. But it would get you a Blue Quantum Fuse and a set of HFTs and/or ECTs. Unless you already have done those its hard to see how any phono stage is going to be a more dramatic improvement.
I like Sutherland. The least expensive is $900 new. I don't know about "dramatically" and it can be subjective but it should be significantly better. Should match well with Pass too. Good cables and power cord are important, as always.
I agree with the above; not for under $600.
With that PA and Pre why would you limit yourself to such an inexpensive phono pre?  I mean you have well over $15K at retail in the amp/pre combo.  What TT/arm combo are you using?
Ifi Audio Iphono 2 is actually dam good for $500ish.
There is a PS Audio GCPH on AG now in your price range. Great phono pre amp with lots of flexibility. Not affiliated with seller.
I've got agree on ps audio gcph. I owned the lp3 long ago it's a very quiet and nice for what it is just a little light in presentation. I use the ps Audio with parts connection mods in another room and when I compare it to a my other tube one at 3 times the price it holds its own. It's very quiet if you keep volume knob between 2 and 3 o'clock. It's very smooth and tube like in my system, maybe it's the mods. Pulls out a lot of information and very full sounding with plenty of headroom, the volume knob is very nice bonus for fine tuning gain. I never use the remote. I'm using it with a Soundsmith 2.4mv cartridge, but I've used it with low out put mc with good luck just can't go to low without a step up.

Turntable VPI Aries Scout with JMW 9 tonearm.
I've had both stock and Parts Connection modded versions of the GCPH. I currently use a Pass Labs XP-15, but I can't let go of the modded GCPH. Actually, the stock one currently listed on AG is priced a little high. They can usually be found for between $500 and $600.   
I'm not familiar with the Moon LP3, but it looks like it's an entry level phono pre and probably the weak link in your analog setup.  You probably need to budget $1500 - $2000 to "dramatically" improve sound quality, but in addition to some of the options mentioned, you might look for a used Musical Surroundings Nova Phonomena.  You should be able to find one within your budget.  Tons of loading options, a wide range of gain settings, and a very "black" background.

For $400 you could also have a Parks Audio Puffin.  I think it's a great value and punches way above it's weight.  I recently picked up a JVC QL-Y66F direct drive turntable from the 80's and mounted my old Shure MX97xE cartridge ($99) with a JICO SAS stylus ($200) and did some headphone listening last night to the 180 gm Led Zeppelin III remaster and... holy smokes! 

The turntable, cart, stylus, and phono pre weigh in at just a little over $1K, but the sound quality was up there with some much more expensive vinyl setups I've heard.  Mind you I was listening through a pretty high end headphone rig (Auralic Taurus + Audeze LCD-4), but the Puffin did not get in the way of the music in any way.  It looks a little weird and it introduces digital into your analog chain which I know is anathema to some, but it's worth giving a listen to.
The Moon LP3 is a fine preamp in the range, but if you want to step up your game, I don't see doing that without at least doubling your budget to $1200 or even $1500+. If you like the Moon phonostage sound – which as I recall has a very neutral presentation – maybe a Moon 310LP is a good one to set your sights on. I had one at home for a couple weeks and thought it was quite good. I considered getting it plus the outboard PSU, but ended up with a Herron phonostage (way out of your budget).
Guess I'll increase the budget and see whats out there used for a bit more.
I have a Parks Audio Budgie that is no longer made but if you can find a used one it’s pretty darn good. The only phono preamp I’ve compared it to was an Audio Research LS1 and I much preferred the Budgie and that was by a large margin. It’s a silly good tube PP that might be worth a try and if you don’t like it you can turn around and resale at no loss and probably fairly fast. Might be real hard finding one though. Can’t speak for the new model as mentioned earlier, but it’s SS I believe and not really a replacement. Not sure why they stopped making the Budgie.
Johnto, if interested there is a PS Audio GCPH on us audiomart for $500 free shipping.
Just took the plunge on an Ayre P5 xe waiting for delivery we'll see how it goes.