If he's having sex with the OW, he may be putting you at risk for sexually transmitted diseases.
His heart isn't in it means that he's not connecting emotionally when ML? That's because he's emotionally divorced. He's being perfunctory, giving it the old college try, but sex isn't what will bring him back. As a guy, I've found it difficult to engage sexually with other women like I did with my wife. Didn't use to, but then again, I've never been as emotionally connected to someone as I was to my WAW.
He's sitting on the fence because there are things about you he wants, and there are things about the OW that he wants. She's filling some emotional need(s).
Having a date in mind as to when you're taking action is a good idea, but his timeline is different than yours. Also, you can't expect an overnight change at the 11th hour. Perhaps it's better to set little goals in the interim.
"After the Affair" by Janis Abrahms Spring is a good work that delves into both how you and he feel, and what is needed from the two of you to reconcile. But it takes two to reconcile, you know. So set goals in that direction: cutting off contact with the OW, enter marriage counseling; start discussing problems. "Her Needs His Needs" by Willard F. Harley, Jr. may provide some insight. According to that book, men typically need:
Sexual Fulfillment Primarily He Needs Her To Engage In Recreational Companionship He Needs Her To Be Good Looking He Needs Peace And Quiet He Needs Her To Be Proud Of Him
Remember not to get enraged, accusative, defensive, offensive, nasty or off-topic. Don't be pleading, begging, crying in front of him. Get counseling yourself if he won't go. Share how you feel with your girlfriends, they can be your support.