Screw fitting to plastic moulding

I have an injection moulded device .. which is to be fixed by self tapper screws. The unit has no ?pilot? holes just ?shallow dimples? to allow screws to
start.
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The unit has same feel & weight as Polypenco I have used in the past - but I have no knowledge of its characteristics other than it is injection moulded, and therefore likely to be thermoplastic
I am fitting the unit through a plywood base which will be reinforcing a lid to collecting drum ? overall thickness of about 12mm
The screws supplied ? No.7 self tappers are not long enough, so I need to use longer screws. I could try and source some longer No. 7 screws, although the No.7 seem quite small for the task ???. Or take 2 different approaches.
#1 drill out the moulding and tap to M4 ? in which case any tips or hints for tapping into such a material would be welcome ? and is the fairly fine thread form of M4 suited to holding in a such a material.
#2 slightly simpler ? I have plenty of No8 stainless self tappers - but would not like to simply screw these in, in case they crack the moulding. From what I find in my ref books the hole for a No.8 self tapping screw is 3.5mm if drilled clean. Any issues with this approach ? the coarser thread may be of benefit in holding in the plastic.
For both options is there a recommended drill speed & lubricant for such material?
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