Try using two flute high helix cutters with a chip load of maybe 0.005" (0.15mm) per tooth and 5000 rpm for a 3/8" (10mm) diameter cutter, depth of cut about 1/2 to 3/4 the cutter diameter. Maybe reduce the rpm if you still get melting.
The idea with plastics is to have a fast feed so that most of the heat generated is carried away quickly in the chip. Four flute cutters do not have enough space for the chip to clear out and you welding packing and melting.
EDIT: Yes I forgot to mention an air blast, very good idea.
An open mind is a virtue...so long as all the common sense has not leaked out.