Problem with breeding traps is stagnant water. There is no circulation and no filtration. The ones with the airstone are better, but sometimes the holes in the trap plug up and don't let water flow freely. When my platies had babies I just moved them to a separate 5 gallon tank. Platies are really bad about eating the fry (at least mine are). I have two adult females and one adult male and I haven't seen any new fry in 4 months. My Sailfin Mollies don't seem to be interested in the fry at all. My female dropped 50+ fry and I don't think I've lost any (at least not that I could see). They also sell tank dividers which might be a good option for you if you don't want to start a new tank. I believe both your tanks are standard sizes that would accept the dividers.
As far as feeding the fry, I've had very good luck with crushed flakes and crushed freeze-dried bloodworms. I see you're going to feed the BBS which is really good as well. Also, the fry eat microorganisms and mollies eat algae as well so they probably would get enough food if they were loose in the community tank, they just wouldn't grow as fast. I've heard that stuff like liquifry can pollute the tank so if you use it do so sparingly. Good luck with the little guys. It's a lot of fun watching them grow up. I just released my 5 platy fry into the community tank last week. They're doing great.