Silicone decomposes, that is, above some 350°C it transforms permanently in useless and stinky compounds like tar, toxic fumes and silica.
If you melt the dirty polyethylene it will be tainted by silicone, the result being expectedly useless. I feel seperating them is mandatory, but rather simple. Though, it needs to develop a few machines which are difficult to pay with recycled waste, hence I asked about the amount.
One polyethylene tube for silicone weighs estimated 80g. Polyethylene from 10,000 empty tubes sold for 0.8€/kg (that would be powder of guaranteed high quality, ready for injection) brings you 600€. Still interested?