Your last post clearly shows that you want this to work and heal mpb in the process (I know that a BS needs to work to heal themselves, but having the support of your significant other helps [or at l want to believe that]).
20WrongsVs1 and Lark are spot on in my opinion and you sound receptive to their advice. I want to say that was exactly what I was feeling during my attempt at R.
"I'm sorry" has such a strong implication of innocence (AKA "It was just an accident/mistake/etc."). Like things were out of your hands and you made a SINGLE bad decision. An affair is not just one would weak moment, not just one wrong choice. It is many times over (possible hundreds, thousands) of making bad decisions.
When my xBF would say "I'm sorry" it fell flat. My response was often similar to mpb or I would just start to cry because I felt like he didn't grasp the hurt I felt.
He called one of the OW "beautiful" in a text. He mainly called me "pretty". When I pointed this out, he started calling me "beautiful" too. But, the word had lost all significance to me. I told him to stop, call me "gorgeous", "goddess", "breathtaking", whatever. JUST NOT BEAUTIFUL. I knew I was way, way, way!! better looking than OW. But that word was vitriol. Just like "I'm sorry". Please, try to find other ways to state your remorse.
But, here now I'm rambling... 
