I have laminate in the hole house except the bedrooms and absolutely hate them. The first time I used the mops and just water or windex w/vinegar which is suggested, they dried all cloudy like yours. I ended up buying a $500 old fashion floor polisher and just spray water and polish all at one time. It hurts my back really bad to have to push anything back & forth. The polisher runs by itself and is easy to quide. Got it at Oreck. Was the only place I found a good one. They also have a cleaner and light polish. Now my floors are really shinny except when I miss a spot and the sun hits it. I can't even wipe up a spot without it being dull. I can't imagine you being able to use Pledge for hardwoods since laminate is not a sealed floor. The Engineered wood cleand up really nice, tho. Much better. Good Luck.
Peg-TX