(1) I believe that you can try making your holes in several steps. I begin with a smaller diameter drill, about 1 or 1.5 mm. I also use less feed, about 20 mm/min. I notice it is much easier to make a hole with a small diameter tool, then work my way up with 2mm, 2,5 mm then 3mm.
(2) Sometimes, I also jog it manually. I first run the program so the machine is positioned correctly over the hole. Then stop the machine, and jog manually in Z direction. Then I can hear when the drill struggles and I can then reverser slightly before continue again. So my own manual pecking if you would like to call it that.
(3) Finally, to bore through a hole you should use -0.5 from the hole bottom. Just want to make sure you have tried that.