Three major points:
First, either you are very paranoid, or you are working in a very unhealthy situation. I want to highlight three things that shouldn't be considered normal: 1) You're worried about your advisor lying in your recommendations, 2) Your advisor is trying to restrict, not disseminate their techniques, and 3) You seem to think you won't be supported in your interests when the lab goes in a new direction. All of these argue that you're not in a healthy spot.
Second, what you are proposing is possible. People can get postdoc offers without advisor recommendation letters. [disclaimer: in many cases, I don't know if there was an informal call - but I don't think so.] It helps to have a strong CV/case for what work you want to do, and how it links to your new PI's plan. Some of it is also luck - some PIs just always ask for letters, and if they do, your explanation is not going to sound great unless your current advisor is well-known as an asshole. (The other possibility is to lean on your own network: people who already know you as a scientist will be willing to skip an advisor's letter.)
Third, it is possible you will burn some bridges by leaving. Having seen this from the side of people left behind in the group, the less notice you give and the more projects you leave unfinished, the more likely you are to burn bridges. However, unless your advisor is particularly spiteful and well-known in the field you want to work in, this probably won't follow you around: academia is a small world, but it is also insular, and big wheels in one field are unknown in another.
Basically: assess if you are really in as unhealthy a situation as it seems, and if you are, it might be worth burning a few bridges to get out of there.