Baltic birch is awesome, but comes in 5x5 sheets, so a taller cab would not be able to be cut from one piece without a seam, not something that would work well. The "A" surface of regular birch plywood would be best if you want ply and not solid MDF. One coat of a good primer/sealer, allow to dry completely, sand, then prime again and paint and you will get a pretty smooth surface without grain coming through (except in the case of where they patch for voids on the surface, that would require filler). MDO uses a fiberglass resin in the surface so it is waterproof, but unless you are getting some low grade MDO, it should be easy to smooth out with one quick sanding and get a really nice finish.
If you just want a smooth grain free surface, a decent birch ply is your best choice, just pick and choose your sheets and be sure to look at the "A" side, not the "C" side which will be way rough. Aside from higher end veneer plywoods like oak, cherry, maple, etc, you are going to have voids. This is why Baltic birch is so great. Chances are you won't run into any problems with the voids in the t-molding though, and if you do, just fill it and re-cut it.