HELP! Question about painting plastic trim

Submitted to Community Café

So, the screen door is built, primed, painted, and it looks nice - yay!  It's our first, and we'll need two more.  We went to Lowe's, looking for trim to cover the screen that we'll staple to the frame.  Found a nice trim on clearance identified as "white oak" - our thought:  We'll paint it brown to match the door, and what a deal!  

Well, mommy... it turns out it's plastic trim. We figured this out after applying a coat of paint - ugh!  Can you say "spotty"?  Yes, we're feeling like dingdongs, not recognizing this product is plastic. 

So, what to do?  I've been on the googler.  I've read about painting over plastic, and I know there are Rustoleum products for such, but which one do we need?  And, what to do with the three 8' lengths of trim that have two coats of brown paint with white spots?  Are they salvageable?

As a relative newbie here, I appreciate and thank you for any and all advice, whether good, bad, ooogly... because that's what our trim boards are - ooogly!