I throw a pipebomb at the rat from ladder to alert the cameras above early and keep throwing pipebombs on the platform since the cameras are more prone to get stuck on each other if you don't. For the jumps through the spinning drill I used livesplit as a timing method. By starting it as I start the level, it will be safe to jump through a drill every 10 seconds for about 5 seconds. For me the safe timings were:
7s-12s, 17s-22s, 27s-32s and so on. It is still possible to skip 1 more drill cycle if you are fast enough but it requires quite a bit of luck with getting the camera down fast enough.