I think the chances of stem rot are a bigger problem indoors, and when the cube is constantly saturated. We have our lettuce outdoors constantly flooded and but for a few instances have no rot issues.

If you keep light from hitting the top of the rockwool, you won't grow the green slime algae that everyone seems to get. That might help.

Stem rot is caused by the pythium bacteria. It is also called "damping off" or falling over disease. The stem will appear pinched at the very top of the cube. The plant will look healthy, until you touch or the wind hits it, and it then breaks in half. I have had my worst problems with damping off in cool, wet weather. I think organic nutrients tend to cause it worse for me, too. If you get organic matter buildup in the cube, bacteria will start growing on it.

If the top of your rockwool feels damp, don't water, it's wet enough. Also make sure your rockwool is not standing in water.
Did you check your ph before you soaked the rockwool?