I don't know why the filter should not be sufficient. Your stocking is pretty near the limit though; a 20g is small for mollies, the female can reach five inches, some report even six inches, and even at say four inches, plus the two platies around 2-3 inches, and the Bristlenose...that's about it. Regular weekly water changes of 50-60% of the tank volume, with a good vacuum of the substrate at each, and keeping the filter well rinsed/clean, should be OK. A new filter is not going to have much impact because there is a space issue, and no amount of filtration can compensate. Keep feeding minimal as you mention, meaning keep them fed but only once a day and not more than they need at that.
