This is one of those dipshit gizmo things auto makers add to their cars from time to time.
No audiophile would shove his/her head into a speaker.
The stereo "image" may be illusive in cars, but good quality speakers, preferably 2 pair, or whatever, should create a suitable psudo-image, when balanced correctly. Good quality, simple equipment.
Disconnect them head whangers. Fit other speakers into the car, pref. behind seats, or in the doors.
I know the MX5/Miata has few options for such arrangements, so fit the very best speakers you can in the optimal space available.
Use 2 way speakers, try JBL or other speakers with excellent low end, and forget about subs, and multi hoodoos, just a stacker in the boot, and a great head unit, with a reasonable grade amp, dont go for BIG power, go for CLEAN sound: less distortion the better at volume.
ENJOY!!
But please dont be antisocial, playing load music where it may disturb others is a pricks act, dont do it. (and you risk coming out to your car and there is a brick through the window)