I'm surprised that the tank hasn't cycled yet.... I wonder what would happen if you just left it alone for a week or two. I'm not saying that that's the best thing to do, but I think it's something I would try if I were in a similar situation.
I would not just assume that it's a matter of over feeding. You don't have many fish in the tank so the extent of whatever over feeding is limited. What I mean by that is that you will feed a smaller amount of food over feeding a smaller number of fish that you will a larger number of fish, corresponding to a smaller overall bio load than a heavier stocked tank would have. Assuming a regular feeding schedule of the same magnatude of over feeding, it would be a constant supply so the bacteria colony would grow to meet the supply.
The filter ought to be able to handle the bioload of 3 over fed platys. What do you have for filtration again? I don't remember, have you seen nitrites?