The Mini Black HAT Hack3r was designed for a pHAT and a HAT or two pHATs, so you're right- there's overlap and the Piano HAT/Drum HAT wont fit together.
All mine have gone walkies, but I don't believe the full-sized Black HAT Hack3r fits two HATs either. It was a productisation of something we used in-house for scoping and testing.
You can use two mini black HAT hackers, and jump the relevant GPIO connections over from one to the other.