If you are looking for the antithesis of "digital" in a digital product, look at the Audionote (uk) line of DACs to mate with a good transport. They make the smoothest, warm and natural sounding DACs that do NOT sound slow and wooley. Accuphase makes some players that also sounded warm and natural (i.e., not digital).
I agree that the Audio Aero is quite natural and beautiful sounding, but I don't think it is "warm" (elevated mid-bass), in fact, it can be a touch lean there. Still, it sounds so good it is worth auditioning. The "cheap" Esoteric, is pretty warm and nice sounding (I like it better than the $15,000 model). I personally did not like the EMM gear (touch bright and cold sounding), and I don't think it is for someone looking for a warm sound.
My "15,000" player is the Naim CDS-3/555PS (outboard power supply) combination. It is reasonably grain free and has less of the artificial hard leading edge to transients, that I associate with digital, than other Naim models, but it is not in the warm, rounded, and "tubey" camp. Worth auditioning, but my guess is that it is not for you.