$375 seems reasonable to gain the full-time cameras and the turn signal activation once & for all. Picture the amount of work that went into those devices.
In fact, I feel a lot better now after someone here discovered the solution and we all gained the option to "throw money at the problem" if that's what you want - when it was really starting to seem kind of hopeless.
Whenever I need to invest $375 or more on something as functional as this, I buy it anyway (maybe skip a fancy dinner or two) because I know that even if it were twice as expensive, the solution would be working on me every time I was towing. Besides, one close-call lane-change or backing into something solid would have me dialing the phone ready to overpay after the fact...
Surrender Rich... and then you can enjoy your self-indulgence for years to come.