With that budget you can pick up an awesome integrated. Depending how much power you need. ARC has a nice tube integrated.
Also…SS units…Something like Pass Int-250 or Luxman 509 or 590. Next level. Huge step up! And no hassle with tubes.
Oh and IMO no tube rolling on CMII will get you to that level.
Another option is to look into separates if you insist on tubes in example, a used Audio Research Ref5 or Ref5SE tube preamp. Pairing that with a good solid state amp like Pass Labs (Class A or A/B) or even ARC’s own Ref75 tube amp will give you what you are looking for.