I don't know if $4k will get you there. Digital does transparency and resolution pretty well at relatively lower price. Analog requires much higher expenditure than the $4k you're talking about. My digital surpassed my analog on transparency/resolution front many years ago, and this with aprox. $7k in tt and phono pre. To bring my analog up to my present digital will take at least $2k cartridge and $7-10K phono pre.
Sure you can improve what you have for $4k, but will that hold up in long run? You'll likely improve your digital in the future and analog will fall behind again, and that's assuming your $4k upgrade measures up to your present digital. I'm in same boat, and I'm going all in on vinyl in future, or simply give it up, no half measures will get me what I want. My take is unless one has funds to go first rate on both formats, concentrate on one or the other in short term, you can always do substantial upgrades for the other format at a later date.