If you are on the budget Audirect Hilidac Beam 2 has mqa support now. Not sure how it sounds, but by measurements via balanced output it should be sufficient to drive even some of the headphones. It doesn't have bluetooth, but if direct connection with phone is not a big hassle, you can try it out.
I know this item, great but I prefer a Bluetooth version. I need it for sport and work also. But for moment only big brand like hiby or fiio are able to purpose dap/dac Bluetooth AND mqa also. I will wait for order one of this.
I would like to try a mqa certified to see the real difference between a version non mqa. I not sure about the real difference between them.