Changes to older system

Actually, wires are the last thing I’d worry about

Depends on if new equipment is desired. I used to take an equipment first approach, now to the point of tuning my equipment with cables. Once a non-believer in cables to sound, it's now one of the main things I've found to make a huge difference. Sometimes to the extent it sounds like I've swapped out the component..

I would try placing the speakers right against the wall to take advantage of boundary reinforcement. That is what my Snell Type A's use. Contrary to what above poster rickysnit claims I find no sonic differences between any cables. Including power cords. I have that NAD 1600 preamp in my collection. It and the 2200 amp are excellent! Yes, you can buy new gear for thousands of $$$$ more but sonic differences would be minimal! I'd consider getting a transport and DAC for what I assume is a nice CD collection. Regarding B&W speakers: they have been known for a long time as having particularly bright treble. Placed against the wall and firing straight out will help alleviate this.

I have experience with an NAD 3150, and some Snell EII speakers. It was a very pleasing combo, and I liked it so much that rather than sell it I gave it to close friends. They play the system daily with their LPs and CDs, and I have somewhat regular visiting privileges.

The Snells, in spite the back firing tweeter, are placed in corners for the sake of furniture layout and owners preference. I think we used brown zip cord for speaker cables. Decent bass, not bright, and sweet vocals. It’s surprisingly good. 🥃

I suppose you play “House” music on that system @zimmer266 ?
😎

I would not do any upgrades to the current preamp and amp. It’s unlikely to make a significant difference and you will never recoup that investment. 
Best upgrade path in my opinion would be speakers. Something like the GoldenEar Triton 3 used. You would solve you brightness and bass issues.
If you don’t want to part with your current speakers consider adding a subwoofer which would fill in the missing bass and tame the treble since it most likely sticks out due to lack of bottom end extension. The challenge with adding a sub is properly integrating it.

I wouldn’t worry about cables. Monster cables are not great but they’re not your problem.

Also consider adding some room treatment. GIK Acoustics make good panels and they’re not expensive. You can upgrade speakers and get few panels and stay within your $2,000 budget.

@ghdprentice recommendation of tube preamp is also a good approach. You can pick up a used Rogue RP-1 preamp for around $1,000. Combine that with a sub as it has 2 pairs of RCA outs one of which you can use to drive the sub

Good luck!