Hi,
don't have either, but, are you just using moxf as a controller keyboard for the bk 7m ie bk7m plays styles and melody sounds, or are you using sounds from mofx for melody at the same time as using bk 7 m for styles.
If you're just using it as a controller, you may just need to change some of your midi settings to keep it as simple as possible.
It sounds like maybe mofx is sending out either sysex or control change messages that might be affecting the bk7m.

I can only go by what my pa3x offers as a controller.
Under midi setup, it has a filters tab.
If yours has the same, try filtering "out " sysex ex messages. Or on the bk7 m see if you can stop filter in .
I can also filter out some specific control change messages.

Unfortunately it's been a while since I've played around with midi ing keyboards and modules together, so a tad rusty on the subject.

Just make sure you keep a note on your setup as is at the moment, just so that you can get back to it, if you start fiddling round with settings.