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
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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