Preamp for Herron VTPH-2A

I am using VTPH-2A with a VTSP-3A. This combination works great in my opinon. Would love to hear a VT-360 in my setup to see if it's a worthy upgrade. You should be able to find a used VTSP-3A as I imagine there are many people upgrading to the VT-360.

With all due respect to some other responders, some of the suggestions for a linestage for someone with a $3K budget, assuming you are willing to spend every bit of that amount, are from outer space, in the sense that you can do so much better for your money.  In the $3K price sphere, you need not even consider a vintage Tandberg or Adcom preamplifier, for one example and not meaning to pick on anyone.  (Those devices may sound fine for a budget purchase, but they were not even top performers when they were brand new.)
Some questions or comments about your stated preferences:
Input impedance "47K or higher".  47K is a standard for MM phono stages, but most linestages will offer at least 50K and very typically 100K on all line level inputs.  Any good linestage should offer inputs that are high enough in impedance to accommodate anything you want to connect to them.  That's one justification for the existence of a pure linestage.  I would suggest you pay more attention, for one example, to the quality of the built-in attenuator(s) in your new linestage.  Attenuators make a lot of difference in terms of transparency.
"Balanced outputs".  I guess you are aware that your Herron phono is single-ended, so you won't get all the benefits of balanced internal circuitry in a linestage, as regards phono.  But if your amplifier(s) are true balanced designs, then it does make sense to drive them in balanced mode. If they are not balanced, then having balanced circuitry and outputs on your linestage won't count for much in terms of making it easier to drive long interconnects. But that does not mean you can't drive long interconnects in SE mode.  I would not require balanced outputs, if your amplifiers are not balanced design. You would also need balanced interconnects to go between a linestage with balanced output and amplifiers that operate in balanced mode.
One guy talked about tubes used in linestages.  If you buy a tube unit, I would stay away from 12AX7/ECC83 in a linestage (way too much gain), and from 12AU7/ECC82 (sound is not good when used as a gain device).  6SN7 is one of the most linear triodes ever made, and I highly recommend it in linestages, but it has gone out of fashion due to size of the glass envelope and the fact that no one is making new ones (I guess).  NOS 6SN7s are still plentiful, however.  Don't hesitate to buy an older linestage based on the 6SN7. Many tube linestages will use one tube for gain and a second tube section per channel as a cathode follower, which adds no gain.  The cathode follower is there to reduce the output impedance, so you can drive amplifiers with low-ish input impedances, which tend to be solid state types. 5687s and 6922s and their congeners are fine too. They offer an advantage in that the inherent output impedance of these types is low enough such that they can work well without the need for a cathode follower. CFs are ok if well designed, but in some cases CFs muddy the sound a bit. No CF is the best CF.  I would look at VAC, Berning, Pass, Atma-sphere, etc, etc.  It's not that hard to design a very good linestage these days, so you have many choices, and I would not be afraid to buy late model used equipment; that's where the bargains are.  Ideally, the device could have one tube, like the 5687, a very high quality attenuator, high quality output coupling capacitors, and an outboard power supply on a second chassis. Or two tubes, like the 6SN7 plus a second tube as CF.  5687/6922/ECC99 are all good high transconductance, low plate resistance tubes that make great CFs.  The number of line level inputs, quality of switching among inputs, availability of remote operation, etc, are what adds to cost

@lewm there are two balanced inputs in his power amp. 

OK, so... I allowed for that.

I'm surprised nobody suggested the Benchmark LA-4.  A friend has one in his system, and it made quite an improvement in his system.  It replaced an Audible Illusions Modulus 3A.  He has a Parasound JC3+ phono stage.  Impressive combo for an all SS system, and well within your budget.