Your thread touches me deeply, as my main concern is leaving my parents behind too. I also 100% understand how important it is to find a comfortable, familiar place for 'the passing'. At first, I wanted to do it at my parents' house too, both because it's where I get that familiar feeling and because I felt like being found by them would be best - the most honest, sincere way to say goodbye. But then, thanks to other members' inputs, I realized it's probably not the best option, as they would have to live the rest of their lives in the same place where I took mine. Not to mention I could be found and rescued.
Now, about you: I know you're considering other methods and maybe you'll find one you can follow away from your home. In that case, would a car parked in a nice spot be an option? Or a camping site, or somewhere secluded close to nature?
I hope this helps you somehow. Much love to you