I have 50, 60 & 75mm bits that someone is welcome to use if needed.

Regarding technique, I have done quite a few with no problem. Get some plumber's putty to build a dam around the hole. Then fill the dammed () area with water. The hole is much easier to start if you hold the bit sideways and just start one corner. Once it is starting to cut, you can straighten it out. Just need to go slow, and make sure you don't run out of water...