Aaron.......you need to have a good sealer primer or a satin finish paint on the walls before you start.
Second - this product when applied correctly will almost completely cover white. It should look even - no streaks. Remember that this product only covers approximately 100 square foot/ gallon.
That is one 12x8 foot wall. That is it. Take a look at how much you were using for those four coats - do the math. An average room will take about 8 gallons.
If you really cannot get this even - but you do like the color - call 1-800-379-POLO - they can give you a color in broadwall paint that is close to your River Rock. Have THD call their Glidden rep to see if they can help you out with the cost of that broadwall paint.