Upgrade my CD player or futile effort?

Budget... new or used?

A dedicated CD transport and an external DAC is definitely the way to go.  I endorse the Audiolab 6000 CDT as a very good transport; there are lots of really excellent DACs.  You don't have to spend more than $2000-3000 total to have something approaching state-of-the-art CD reproduction (note that I said "approaching" - not "reaching").  I am sure you will be a lot happier with CD sound than you are now.

I went with the RME ADI-2-DAC fs that hshifi mentions and love it. It has more features surrounding the actual DAC than the competitors, but that might be more than you want to deal with. I am in total agreement with the above advice that you change one thing only to start with. That would be the DAC. Keep it separate from the transport player so you can upgrade either as you desire in the future. I even think the Topping Dx7 Pro would improve your system and it would cost a lot less to try. Buy from a place where you can return it, no questions asked, if you don't think it is a major improvement or to your liking. Plus, it comes with a nice headphone amp, so you can find more places to spend your money in the future. :)I have ripped all my CDs and find I rarely listen to either the actual CD or the ripped version. I started with Qobuz and thought it was great, then tried Amazon Music HD and never looked back. It sounds great and it probably has any CD you have plus tons more. It has a great interface to pick an artist and it lists all their hits to see if there are ones you like. It also has so much artist and album information to get lost in for...you pick the timeframe.  Don't get me wrong, I am not a Jeff Besos' fan, but there is a reason why they are the largest at what they choose to do. Just my opinion, but I chose to not buy into the MQA/artist platform (Tidal).Have fun!

@baylinor, I haven't read this entire thread. So, if someone else has already touched upon this or if you are already aware of this, I apologize for the redundancy.

Assuming you are using reasonably good interconnects with the CD6005 and using it as a player and not as a transport, do you have it switched to its "Audio EX 2" sound mode? This is covered in the manual and easy to do (i.e. the push of a button). "Audio EX 2" sound mode will give you the best audio the CD6005 is capable of. Will that be better than your vinyl play? Assuming reasonably good vinyl care and play habits... no. However, "Audio EX 2" sound mode will be a touch better than what you're getting now. It will be a subtle but noticeable improvement.

Another option is to use the CD6005 as a transport with a better DAC. However, the DAC in the CD6005 is pretty good. IMHO, it's on par with the MAC DA1. Will you find the audio produced by a better, high-end DAC better than what you're getting from your vinyl play now? Well, only your ears can decide that. Personally, pound for pound, dollar for dollar, I have yet to hear any digital media that sounds better than a good vinyl set-up.

You guys are the best! A lot of very good advice from many different directions. The one that resonate to me is do one improvement at a time. Been guilty of not doing that in the past. The other one that comes back most often is get an external DAC and keep the current  transport. I am totally in line with that. I spent quite a few hours now reviewing my options. It seems that the starting range that may please me in a DAC is $700. Of course it can get better from there, but that may be enough to get my toes wet. Anyhow, so far I am considering the following:
-Schiit Bifrost 2.
5 year warranty and 15 days return!
-Denafrips aresII
-Topping D70S, (the D90SE may be too revealing for my system)
-Musicians Pegasus, sounds like a winner, but reliability questions with a brand new company concern me. 
Some other DACs in that price range mentioned here include headphones preamps which I don't need since I have the Schiit Asgard 3. No sense paying for that. As I said earlier streaming won't be for me, I need the tactile part of my music collection. Over 2,000 vinyl and about 400 CDs. 
So just need a simple no bells and whistles straight DAC with RCA out and coaxial in (no optical, got it!) and will hook it up to my Prima Luna 100 tube preamp. I just have to decide between those based on sound characteristics which can get overwhelming in the many reviews. Please chime in some more if you experienced the sound of any of those. Thanks to all.