I hope the lacquer thinner works. In my experience chemicals like lacquer thinner and acetone melt some plastics, so test in a tiny area before you commit to big areas. Yes, they work great on the paint, but once you rub through, when those chemicals hit the plastic it starts to go wrong.
What happens to the plastic when using these chemicals is it seems to soften and melt. The molded plastic often has a smooth surface that begins to show streaks from the rag as the chemical is applied and the plastic rubbed upon. Once it all dries and hardens, the streaks are still there.
I've had good results with IPA, isopropyl alcohol. but it's slow. I've been able to clean several items that were once shiny plastic, and covered with rattle can paint. I presume that paint is lacquer-based. With soaking in IPA, and using something also plastic, but hard, like the edge of a credit card, to work through the paint down to the plastic, I was able to remove the paint and still have a shiny plastic piece underneath. There was lots of rubbing with a rag. It was slow, but it worked.
But those were plastics with mostly flat areas. I did a set of those cuda grill strips, with the red stripe, that were painted over with flat black many years ago. In the end, I was able to save about 50% of the original red stripe, and have some decent looking trim pieces. That took me 6-8 hours to do.
I cannot imagine the amount of time and detail such a process would take on the cowl vent grills.
If you can find something to soften the over-paint, without affecting the plastic, that is the magic substance, right there.