Agreed...
I would agree... the JJs do seem to sound a bit less aggressive, and perhaps a bit more "smooth and refined" - than the stock tubes. Probably good with brighter phones - like Grados, or ATHs. Though, I still like the "aggressive" sound of the stock Philips, especially with my Senns, which need more "life."
You might try the NOS Amperex 6DJ8/6922s - will sound warmer, smoother, less brilliant highs - but... they come at a bit of a premium. The Russian 6H23N-EBs, or 6N1P-EBs, may also sound less "aggressive" in the upper mids and highs - while still providing solid bass, and rich mids. Though the 6N1Ps were a bit too "mellow" for me in the highs with my Senns. These both sounded great in my XCAN v3, which has a bit of a bright sound anyway. They might be a good fit in the NM version - which may have a bit brighter sound than the M version of the M24.
You also might try "mixing" the tubes a bit - for example, using Stock tubes in the tube DAC circuit, and the Russian tubes in the Line Stage circuit, and connecting your amp to the Line Stage output. You might find the Russian tubes in the Line Stage would mellow the bright sound of the Philips tubes in the DAC - they seemed to do that in mine. This configuration gives you more gain, but you can "tune" it to your preference (turn down the Lines Stage volume POT, and turn up the amp volume POT, etc.).
In the end... you'll likely have to "experiment" until you "get to your sound."