Today Apple released update 12.4.1 for iTunes.  I have been testing it, and not only does it work fine with BitPerfect, it also fixes whatever was causing the problem with “Minimize iTunes Interaction” mode that occurred with iTunes 12.4.0, so BitPerfect users who prefer that mode of operation can feel confident enough to try enabling it again.  However, it will still be necessary to disable and re-enable BitPerfect after making the change in order for it to come into effect.