I do soil grows using an assload of little pots as well so i know exactly what your asking,what your thinking is that due to the size of the pots you need to flood the soil making a huge mess every time you water,am i correct ?
This is gonna sound ghetto but it worked for me until i could finish my 1st grow & rebuild the room,i took milk crates & placed them in rows,then laid lumber over the top of them & placed the pots on top of the lumber,this raised the pots about 14 inches from the floor & the spacing between the milk crates allowed for me to easily mop up the excess water.
Ive since rebuilt the room,i built a new floor from plywood making it slope all to one corner,i then covered the floor with linoleaum,in the corner i put a shower drain & connected the drain to a peice of black plastic hose much like used for a sump pump then put the hose directly through the wall leading out of the building,it looks like a sump pump hose from outside.