That is an interesting idea for certain. A common way to use a speaker amp / headphones is with a cable that has speaker taps tied to a TRS or XLR jack. Planar's like HiFiMAN HE5, HE6se, etc.. are really impressive using a speaker amplifier. HiFiMAN makes a neat external device utilizing the speaker taps to 4 pin XLR. A balanced cable for use with HD650 would be needed.
https://hifiman.com/products/detail/84Not certain how this would work with a Stereomour II but it may be a relatively easy task to do a DIY box of similar function to optimize matching. HD650 is not very hard to drive compared to higher end planars.
I modded an old Emotiva A-100 50W speaker amp a awhile back to drive my HE6se. I used a 15/16 stepped drill bit to punch a hole into the faceplate and then used a 4 pin XLR jack wired directly to the speaker taps internally using twisted wire. Works beautifully, dead silence, and gobs of scary power. I wouldn't try doing that with a stereomour without knowing more information if it's wise to do it or not. In my case, I have Crack and SEX amps for headphones use and have plans to use Stereomour dedicated to speakers.