One of the differences between the original Classic and the new Classic is that the original Classic was a 2 channel amp (left and right channels). The new Classic is a 3 channel amp (left, right and ground channels). I find that adding the ground channel increases the blackness of the amp's background and substantially increases its effective dynamic range as well as the size and coherence of its soundstage.
A 24v elpac will supply plenty of power to a PPA with 637's in the L/R channels and a 627 in the ground, so it should be no problem for the new Classic with the same opamps. A 24v elpac powered my new Classic with three 627's with no problem. I then switched to a self-built AA power pak with 16 NiMH AA's in series for cleaner, quieter power.
Does your new Classic have a sufficiently high gain to permit the use of 637's in it? The 637's are only minimally stable at a gain of 5, and the higher the gain, the more stable they are. I've read DIY folks recommend a gain of 7 in order to use 637's stably.
I find three 627's to give a very fine Burr Brown sound to the amp. I find the new Classic, with AD8620/10 opamps, to sound significantly better than the original two channel amp with an AD8620. I also find that the new Classic with AD8620/10 opamps is positively synergistic with canalphones.