Should I make any changes?

Digital audio has progressed rapidly in the last 10years.  So modern DACs typically is significantly sonically superior than those from the past.

A CD player has both a transport+DAC.  In the 3-4k range it’s difficult to find high sonic quality CD player.

Since the OP already has a transport (assuming it’s up to the task and not a sonic bottleneck), suggest getting a stand alone DAC.

Yes, a DAC upgrade is definitely in order. I am with @ghdprentice , it is a good time to switch to streaming, you will be glad that you did. Schiit makes a good range of DAC’s, from the same guy that designed your Theta. I like the Innuos streamers, good software, good support, great sound.

Ayre CX8 with an optional USB module and a Node Icon should set you up for top tier CD playback and streaming.  The Ayre would need to be used to fit the budget. 

Should you...should you not?

Do you even seriously listen to..or enjoy listening to, appreciate specific artists and so on?

Or....is it all.. genre background music?

I listen mostly to jazz and classical music on CDs so I retained

?

I suggest one of the current Transports and Dac's that are receiving the attention of the informed audio crowd without breaking the bank.