@itsjustme
I suggest hearing digital from a great, old analog recording, well mastered (interestingly, most will be red book, not HD) such as the old verve, blue note or Mercury stuff.
I have to say you nailed it with this observation. This has precisely been my listening experience. Many of the jazz labels from the 1950s-1960s if remastered with care and skill will sound natural and wonderful. So much sucess is dependent on the recording itself. For an example, Contemporary Records (Old school west coast jazz label) Prestige, Riverside etc. Just to mention a few to add to your list.
Their Redbook CDs sound absolutely beautiful and engaging via my CD transport and DAC pairing. I think some digital components chase the detail aspect too much and miss the forest (Naturalness) for the trees (over emphasized artificial detail)). But without question there are some very capable and well implemented digital components that will get the job done in an exceedingly musically -realistic accomplished manner.
Charles