You might try finding an old screwdriver with a blade small enough to go into the lower bolt holes, this shows you that the blade will fit into the upper holes.
Then heat the screwdriver blade hot enough to force it into the broken plastic bolt stubs. Then allow the screwdriver blade to fully cool.
If all works as planned you should be able to back the broken stubs out with that screwdriver.
Worst case, just center drill the broken plastic stubs then chase the holes with a proper sized tap.
Or drill the holes out to the size of your new license plate bolts then use washers and nuts on the back of the mounting plate.