It sounds to me like you are doing exactly what should be done. You are loving him and caring for him in a home situation. You are not subjecting him to unnecessary tests. When his time comes, you will know. I didn't believe it, but you will.

And you are not crazy!! Anyone who loves their pet as a part of the family will agree. We all go through those same thoughts as our faithful companions come to the end of their time. It's sad, but is the most caring thing you can do when that time comes.

My thoughts and prayers are with you and with Rex right now. Love him and enjoy him while he is here and store memories to help you through the hard times.