OK, newbie weighing in with an opinion.
While a properly executed gasifier can cope with a small amount of plastic within it, I personally do not see it as an idea I want to get into. The whole idea of "driving on wood" is tainted when you start putting in the waste products from the petrochemical industry. However, it has intrigued me so I have researched it further. Back to that in a bit...
On a side note this was battered around at work a while ago. Stick with it, I am going somewhere with it. Having a 50cc Peugeot 2T moped it is capable of mixing its own 2T oil with the fuel. It has a very small oil pump which drip feeds the carburettor with 2T oil. The thought which we hammered around was to use this pump to "drip feed" black diesel (waste engine oil) into the fuel line of a diesel vehicle. I know there are problems with implementing such a thing and we really thrashed those points to death. Anyway, the point of it was to use waste engine oil to nudge up fuel economy while being quite discrete about the whole deal. Mainly because using waste engine oil as fuel on a UK road will get you in a whole vat of trouble, so feeding it in right behind the fuel pump would need a skilled mechanic operating on a tip off to even spot it. After reading about Mr Gilmores excellent Simple Fire the thought of a moped oiler was rekindled. Having a vertical inlet would allow waste oil, or even a more environmentally friendly vegetable oil to be drip fed right into the reaction zone. A theory that I am willing to try if I can get to build a most excellent Simple Fire. I'm sure that it could be adapted to drip oil into the reaction zone of a downdraught gasifier after a little thought on implementation.
Anyway, back to the plastics issue. After watching "Back to ze Future" (sorry to any of my Germanic European cousins, I couldn't help the pun) and seeing a Lupo being substituted on its fuel by a plastic pyrolysis gizmo I searched further and found a PDF from an Indian intellectual heavyweight who did the research on running a diesel on pyrolised plastic. Its not that long but contains some real raw data. There is no meaty info on the setup so no way of copying what they used but it is inspirational to read. If your interested the link is below (hope it works). I have a PDF copy of it but can't fathom out how to get it on forum. If you want a copy then email me. It may help to watch a few episodes of The Big Bang Theory first to get you used to the level of intellect in its content!