I go front to back as mmuch as possible. Once I land on a source, I simply go from there. PCs, ICs, etc.
Doesn't sound to me like you have settled on a CDP yet.
I'm prone to getting as much of utterly revealing and resolute while still being listenable or musical, if you will, in any source unit I'll buy.
The matching or mismatching thereafter is to what lays downstream and my own preffs for the end result... as I'm not a dead neutral 100%er sort.
It is all a mix to be sure. Cables do have an effect, but I tend to use them to enhance rather than to ameliorate or cover up what is errant there... now, anyhow. This cabling thing gets loads easier when the components are better, and better matched IMO.
Try a couple more CDPs. Money spent well there will sure pay dividends later on.