Applying for different PhD position: letters of recommendation
Have you ever tried discussing your concerns with your supervisor? It isn't very clear from your previous post and this one. As you mentioned in your previous post that you are quite indispensable to his lab, hence, communicating your problems might make him want to fix them. I had a friend who was on the verge of a burn-out while doing his PhD. Like you, he was also handling multiple projects at the same time. One day he walked upto his supervisor's office and told her that he would like to leave the lab because of certain issues and would like her to support her PhD applications elsewhere. She thanked him for bringing up the issues and did provide letters of recommendations in a timely manner. At the end he continued working in the same lab but the supervisor was much more accommodating of his requests. 

Now this might/might not happen with you but making your supervisor aware of the issues seems to be the best approach in my opinion. Especially when your field is interdisciplinary and it may be difficult to change departments without bumping into one of his acquaintances. It would save you from a lot of headache and mess if you just tell your supervisor that you are considering changing labs and want to explore a different (positive and motivating) environment for your PhD. Make a draft of what/how you want to say it. It will take some time but will be worthwhile in the long-run. And if you think he might say something and change his mind later on, it might be best to communicate via email. This will serve as a reference to explain your situation to your potential supervisor/grad school.

All the best!