I've decided to return the phrase "I'm sorry" to my vocabulary in the sense of "I feel sorrow for your pain [and hope the sharing of your pain and knowing you're cared for makes it slightly easier for you]". To make this more effective, I intend to continue my attempt to replace "I'm sorry" meaning "I apologize" with "I apologize".
I apologize to anybody to whom I've responded to "I'm sorry" with "It's not your fault" when they were clearly offering sympathy rather than apology. This is neither productive communication nor is it actually clever, as I seem to have believed. I intend to stop this habit, and I encourage others to do the same. I would appreciate assistance with this; it's highly habitual, so if you could gently point it out and, if necessary [it probably won't be], remind me of this statement, that would be helpful.
The lack of being able to say "I'm sorry", especially as I have largely failed to find a suitable replacement, has impeded my successful communication for years. It's time to stop muddying the waters.