System advice

I second Sbank's suggestion. Isolation ( both electrical and physical ) and damping tweaks have done wonders for my systems. Premium power cords ( within reason ), a Porter Port, an Isoclean power bar ( these aren't cheap ), BDR cones, Herbie's Audio Lab footers and tube dampers, Bright Star Isonodes, maple platforms and isolation transformers are all very good bets.

I would spend every cent I could on a top notch preamp and go from there as funds allow.

The 2ce's should be able to give you that Live in Your Living Room sensation, no problem. I strongly preferred mine with tube gear. In the Chicago area, you ought to be able to find some different integrateds to try out. I think appropriate tube gear may bring them more to life for you.

Replacing the Anthem gear seems like a good plan. A tubed integrated is a great suggestion. I assume you must have a phono section in the Anthem preamp. So, if the Anthem is sold, you will need a tuner, a phono preamp, and an integrated with at least 3 inputs to accommodate these components plus your CD player. Your budget is $2000 plus whatever the Anthem stuff brings you.
As an alternative, I would consider finding a vintage tube preamp like an Audio Research SP-6b ($600-700) with an Ayre V-3 or a Rowland Model 1 ($1100). Then find a nice vintage Japanese tuner from Sansui or Kenwood for around $200 and you're done. Nothing in this package will depreciate and everything can be upgraded in turn. There will be extra money for cables, isolation, etc. if you wish to explore them. The downside is no remote. I have found that the combo of tubes, phono section and remote control in one unit is fairly rare. Who knows of any?

I had the same amp wih 2ces, not sigs - the anthem is a good value amp but didnt mate well with Vandies (I had B&K preamp comparable to Anthem pre) The best I've heard the Vandies is with The Jolida 502brc I have now (Tube integrated)and very careful setup following the manual when you get the placement and tilt right you'll know it.....