Rolling Mullard 6DJ8 into GE 5670 Application

Yes, the parameters that work for a designed 6SN7 would not tend to damage an E88CC.  But you could get some improvement by increasing the plate current, which has to be done in such a way as not to exceed the recommended plate dissipation for an E88CC, which might mean just lowering the plate voltage.  Best to leave well enough alone.  Many would argue that the 6SN7, as was, is one of the lowest distortion triodes ever made.

I know I sound pedantic, but the 6SN7 and E88CC are very different tubes electronically, even if you can find an adapter to make a 6SN7 "work" in a socket wired for an E88CC. The E88CC is a high transconductance tube with a mu of 33. The 6SN7 is a medium mu tube (mu about 16) that usually is run with less than 12mA of plate current, usually much less in fact. The E88CC likes more like 15mA of plate current. Also, because of its high transconductance, the conditions that work for the E88CC could conceivably be destructive for the 6SN7 over a short period of time. If you have a schematic, and if you know how to modify the circuit parameters to suit the 6SN7, then that’s fine. Otherwise, I would leave well enough alone. If the tube is serving as a cathode follower in the DAC, the E88CC is actually a better cathode follower than the 6SN7 (because of characteristics mentioned above and other characteristics), which would be another reason to leave it alone. Of course, you can do whatever you want; I am only giving you some facts to think about.

 Buell, from your post I gather you may have either substituted for a 12AU7 or rolled 12AU7s. Which is it?

The issue for me is not how either tube sounds, but whether or not the two tubes are comparable in terms of their transconductance, mu, and plate resistance, such that you could plug one into a circuit designed for the other and still get the most out of the substituted tube.

Depends upon what the tube is doing in the DAC.  If it is supplying gain, then yes you'll hear "a difference". What sort of difference is impossible to say without knowing the circuit and even then it would be a guess.  If the tube is just acting as a cathode follower that drives the downstream linestage or amplifier, then the difference afforded by different tubes would be much less profound or maybe not noticeable.  Are you sure the 6DJ8 is electrically compatible with a WE396A and/ or a 5670?  I am totally unfamiliar with the latter two tube types.  There's more to tube replacements than just having a correct adapter.