OK, I understand your problem, and having advertised the Meinls in earlier posts, I feel somehow responsible ...
Well, perhaps you different tuning with the tumba. Of course, a too thin head makes a hollow sound (as a too thick one gives you the magic sound of cardboard - as I had to experience..
But anyway, Meinl does not use very thick heads these days. I don´t know why- emaciated water buffalos? Too good shaving blades?
To be srious, my experience with those Meinls is, it´s difficult to fond the "round sweet spot" in tuning - just try.
I wonder if new heads do any good , expensive, you´re right, and if not pre-mounted, there´s trouble with the sizes.
I wonder if I´ve been much help...
Good luck anyway!