I need to screw 100 to 120mm, gauge 12 (5.5 mm diam) screws onto plywood on top of hardwood (joists)

The dewalt no. 10 screwdigger that I have drills a pilot hole of 3.5 mm which seems to be appropriate for gauge 12.

The problem is the length of the screwdigger; the available length is about 65mm including the countersink. This means that the last 35mm (for the 100 mm screws, 55mm for the 120mm) will not have pilot hole. Is this a problem? Isn't it too hard to drive in the screws in this situation?

Are there any longer 3.5 or 5mm wood dril bits or screwdiggers? I have not found them?

The general question is, how does one prepare the hole for long screws on hard wood?

In my case, one option is to lift the plywood and make deeper the holes on the joists, I don't like this very much because it will be difficult to replace the board with the pilot holes perfectly aligned.