Bummer...I know this is going to sound just plain wrong..but I think you need thinner coats. Here's how I varnish on my boats, maybe there is a clue here that will help....
First..with varnish, I wet sand lightly w/ 220 grit between each coat to remove dust nibs. You will probably want to go ahead and remove the runs at this point on your project. BTW...I don't skimp on varnish and get a good marine spar like Epiphanes, Interlux Schooner, etc. I think it pays in protection to the epoxy and durability over time.
Wet down the floor with a misting bottle if you are getting a lot of dust. In addition dampening anything lying around, I think wetting the floor helps with the static electricty. It seems like fresh varnish is like a magnet.
Strain your varnish into a separate container... and never dip your brush into a can or put leftovers back into the can. Seal the can good.
Use a foam brush to apply the varnish. use long strokes with a crossing pattern and don't overwork. This should leave a light coat that should not run at all.
Let dry, then repeat three or more coats, wet sanding in between. The more coats you put on, the deeper the finish will be and more protection you will give your epoxy. I ususally put about 6 coats on new work.
Hope I mentioned suomething that helps...
