get a board of 18mm plyAdding wood sounds perfect - but then how do I do the same job again 100 times?
cut it to fit inside the box, so it goes down to bottom -chamfer edge as needed, put it in place, then screw a batten on the ply so it sits against the top of the box lip
then take out the ply, drill 4 holes (size of centre drill in hole saw to match the position of the centre of the holes
then drill the holes
the problem you have at the moment is when you drill in the centre drill makes the hole bigger so there is no centre guide for the drill and it wobbles