The table I played on most often for a while was a GC3 at Shoreline Billiards in Mountain View, California. (Table 4, for regulars.) The slates were not doweled. The foot section became hump-backed so both sides would roll towards the cushion. Also, you could see where the seam stuck up in the middle of the table. John Wright, a local table mechanic, drilled through the slate and put a long screw in so he could pull the middle of the slate back down. I have no idea if that was the right way to do it, but it worked.
A small nitty point... The two characteristics you need are "flat" and "level". A flat surface could have a 10-degree slope. Flat means the surface is all in one plane. Level means that the surface is perpendicular to a line drawn to the center of the Earth. A slate that is not flat cannot be level. Parts of it can be level but not the whole slate. In the case of Table 4, two of the slate sections might have been both flat and level but the foot section was neither.