As you may know, there are a lot of paint strippers that will attack plastic, so test whatever you decide on a small section on the back of the plastic part if you can first.
Chemicals like lacquer thinner, and general paint strippers will aggressively attack plastic. Some other paint stripper chemicals you may have heard of like brake fluid are a little safer but will actually ruin the chemical makeup of the plastic and change the integrity of the plastic - still not good. While other chemicals like naphtha, denatured alcohol, and clothing detergents are mild and fairly safe.
I am a former product designer in both metal and plastics. I'm also a professional modeler. I have to often strip plastics in a safe manner and do it efficiently and hopefully quickly. If I had to strip something large and plastic with rattle can paints, I would first use something simple, safe and efficient like....are your ready for this...Easy-Off Spray On Oven Cleaner. The good ole' simple bright yellow can your mother used. Its cheap, easy to find, and most importantly easy on the plastic. EZ-OFF will attack aluminum! So, be sure to remove all metal trim first if possible. Test a small area of stainless before you spray it. This is not a fast stripper by any means, but its safe on plastic. I've had plastic parts sitting in EZ-Off for a couple days. Find or build a container around your part (something plastic like a garbage bag, don't use alum.foil!)...spray it on and let it soak in the foamy solution for a good 3-6 hours. It may take several spray applications to keep the foam wet and active during this soaking time. If after several hours you don't see any "activity" of loosening paint, then let it sit overnight. It does wash off easily with water. If nothing happens over night, try some PINE-SOL, another cleaner your mother used. You can leave plastic parts soaking in a total bath of PINE-SOL for months. Pine-sol is very safe but slow to strip and sometimes after weeks of soaking in Pine-sol nothing happens. Lastly, try Naphtha (found at any hdwre store) again testing in a small area on the back if possible first. Naphtha can be aggressive on a few plastics, but others it is quite safe. So, test it. If those 3 chemicals do not work, you may need the steel wool treatment.
My 2 cents.