Well, depending on the fish you get, it really does matter that yours isn't fully filtered.
Were I work, you can ask any one of us the number one thing we always do for our tanks, and that's over do the filtering. I don't mean, create a whirlpool effect, but more is always better. Yours isn't strong enough to fully cycle the tanks water. With I do suggest is getting another 20 gallon, have one on one end and the second at the other end. This is how I have my tanks, one 60 gallon w/ two 60 filters, and one 20 with a 40 filter.
I used cycle and noticed that it clouded my water, so it may be from the product. Many people told me it was basically over priced water : ( So it might not hurt to discontinue using it.
Also, check your water quality, super hard water or calcium build up can cause foggy water.
How long have you had it up? You could have "new tank syndrome", basically cloudy water. Or an algae bloom. You can use a water clairifier for any fine particulate, but it won't help if it's algea.
Also look close, sometimes algae will be growing on the walls, almost clear, slightly off white, making a sort of film on the glass.
Best of Luck!
Edit:
I wouldn't suggest taking the ten from the barbs. 1)they need it, obviouslly. 2) you can't take it form them temporarily, b/c it will take much longer for the larger tank to be cleaned and cleared. 3) The barbs will attack and hurt the guppies, as you say they were already doing.
Can you instead, take the filter cartridge from the little and put it in the big? This will help transfer some of the good bacteria already established and jump start your cycling for the larger one. You can also take come rocks from the established tank and put it in the larger tank. Also basically jump starting the syscling system.