I had this dilemma when building my theater
a few years ago. I was trying to select ceiling tiles and started off with just some samples and small amounts of paint. I ran into all the aforementioned problems:
1. Consumes an awful lot of paint ($$) and still there are white speckles in the pits of the acoustically formed surface.
2. Takes a lot of time to work the paint into the pits. While I could start with a roller, I would need a brush to get into all the pits and grooves.
3. Probably changes the acoustical properties of the tile given the now smooth layer of paint on the formerly rough surface.
4. The tile warped. (I didn't think of painting both sides which would at any rate cost more).
I eventually chose hardboard (Masonite) instead of tiles. Panels of appropriate size could be cut and then be painted easily prior to installation. A simple paint roller job. I guessed at the time that by the time an acoustical panel was painted to cover all the white, the acoustical properties would be almost the same as a flat panel.
Because there wasn't enough headroom in the basement for a full suspended ceiling with grid, I omitted the grid and screwed the panels directly to the joists (actually set off with small blocks to clear pipes that were clamped directly to the joists.).