Upgrade My Turntable - How Much Do I Need to Spend?

@OP. Issues with turntable setup/maintenance are frequently overstated. Non- suspended subchassis turntables need close to zero maintenance apart from an occasional belt change and, possibly, a drop or two of bearing lubricant. Similarly, a cartridge that is properly installed needs nothing until its stylus is worn out.

Taking account of your budget, a Rega Planar 8 would be a good starting point. If you up your budget to above your $4k suggested limit, the Technics SL1200G is excellent and totally bulletproof in terms of reliability - direct drive so effectively maintenance free.

If you want a suspended deck, the Michell Gyrodec a good relatively fuss free choice.

@lewm 

If you have a noise that is say 24 dB down in the left channel and add the noise, 24 dB down, to the right channel, the combined volume will be 21 dB down or double the power, not double the volume. 

@whart 

Isolation is ALWAYS necessary when it comes to turntables. Turntables are vibration measuring devices and they do not care where the vibration is coming from. The environment is full of extraneous vibration from your refrigerator kicking in to the truck running down the street. People who live in NYC are very familiar with this problem. I call it environmental rumble, it is even a problem if you live in the country, only not as bad. People with turntables that are not suspended. Put your stylus down on a stationary record and turn the volume all the way up. You will see your woofer moving, shaking. The turntable is measuring the rumble in your environment. If I try the same experiment on an SME or Sota you will see nothing, no shaking at all. Any unsuspended turntable needs to be put on a suspension platform. With the weight of the turntable the resonance frequency of the suspension should be below 3 Hz. 

The answer is that when you sum the two channels in phase you cancel signals due to vertical deflection of the cantilever. So Elliot was in error to claim such noise is doubled.

I like Stereo5 recommendation because it is a great tt plus, you have a removable headshell to change out cartridges in the future. 
you have a good tt. I might recommend you upgrade the cartridge to a Hana SL or a cartridge HANA ML. They both come on a high output in case you only have a moving magnet input. Next is the phono stage. There are some killer phono stages out there especially in the used market. Vinyl lovers are nuts. We always want better and better. The one I use now is the Hegel V10. Down the road I will get the ARC Ref 2se. I love a tube phono stage. 
if you can wait a little bit you are going to start seeing Rega P10 tt on the market because the new $12 NAIA  has just hit the US. First hand I know this will be much better than the P10. Also, Ortofon just came out with cartridges that fit Rega without using shims. Most important is the setup of the cartridge. Especially when it comes to Zenith,Azimuth, and Anti-Skate. It is worth it to have it set up professionally. Once you get those three correct it is easy to dial in your turntable to your system and ears yourself. Buy a River Stone VTF scale from Amazon to take care of that yourself. 

You don’t need to spend 4 grand. My friend has the Technics SL-1200 GR and it is an outstanding table for about 2 grand. It also comes in black ( SL-1210 GR). It is a definite upgrade to the table that you are now using!