Take a piece of silver steel the diameter you need. (Or turn a larger piece down) Drill a hole in the end the size of the pilot you want.
Now get a small triangular file and file cutting teeth into the end. Make sure you file them so that they will be cutting when the cutter is rotating in the standard direction. The idea is to not leave a flat on the top of the tooth, but also not to file too much off any one tooth, as ideally you want them all to be the same height so they all cut. Note that you don't need dividing equipment, they don't all have to be exactly the same depth or width, just the height of the cutting edge should match up.
Now if you were going to use this on metal, this is where you would harden and temper the silver steel. For polystyrene it will probably be fine if you leave it as it comes. If you use it a lot the filler in the plastic might eventually blunt it, but then since you didn't harden it a few more strokes with a fine file will let you sharpen it again.
So now make a little pilot, and fit it into the hole in the end with a bit of Loctite or similar. For cutting this sort of plastic probably the cutter could be twiddled in your fingers.
However…you say the holes are currently 1/16 deep and you want to counterbore them to .070". That is deeper than the existing hole. The only way to do that with a piloted cutter would be to deepen the existing hole first.
I have some cutters like this that I made nearly thirty years ago to counterbore Stuart castings where the studs go through…they are still good.
John