You know... all I wanted out of this post was basic information on what's hackable and what's not, how, and potential solutions for anything that is an issue. Sadly I've failed to get any of that.
A solution for the FOB is that $10 sleeve from Amazon, but I'm no closer to figuring out anything regarding the Bluetooth.
For bluetooth, turn off bluetooth on your phone when you don't want to use it as a key. There's no good passive countermeasure there because if you put your phone in a anti-RF sleeve, you won't be able to use it or receive calls/texts.