When I first started growing I was ask to do a bunch of clones for a friend...ended up doing over a hundred clones on my first attempt at growing.
My area was limited for stores and supplies so I had to find ways to over come some hurdles that came up. Here is what has worked well for me.
1- I cut the cubes down so they don't hold as much water. I kept having problems like you where they stayed wet far too long and either started molding or took forever to root.
->Cut the cube(s) into a tube shape.
->Cut the tube(s) in half to make 2 pucks from 1 cube.
->Filled in the center holes with the scrap pieces from cutting into tubes.
2- I then made up trays that would allow the puck(s) and cutting(s) to be raised up so I couldn't over water as easily.
3- I put the plant cutting(s) into dry puck(s) and set them in a dish of water until fully saturated. Usually takes about a minute or less. (I give everything a quick spray down once the tray is filled up and put dome on...spray the dome too)
4- Some times I don't use the top/dome, but for small or fragile cuttings it helps.
->When pucks dry 80-90% (not 100% dry) I then soak the pucks again in a dish like in step 3.
->Don't spray the cutting(s), just the dome, daily if no condensation is seen.
->After a few days start to remove the dome from short periods to longer periods of time over the course of a few more days until its no longer needed. (If cutting starts to wilt, cover back up right away.)
Within 10-14 days you should start seeing roots come through the sides of the puck(s).
Hope that made sense...lol
Good luck and happy growin'