I know my H had told me that he had no contact with OW...only for me to find some emails (he left his email open and for the life of me I don't know what impelled me to look)between OW and H...now this was about 8 months after he moved home...and about 5 months before he was able to say he loved me again...
In the emails he professed his love for her always...said she saved his life...wanted to talk on the phone with her...evidently at one point she had tried to call his old office number...anyway it made me so sick to see this...but she did mention she always knew he would go back to me...and that she was with a really good man herself now...
What I am trying to tell you is it takes time for them to get OW out of their system...totally...this took place nearly 3 years after they ended the A!!!
As far as I know there has been no more contact...things with H and I are continuing to improve...
So in your situation I think it is good that you are willing to make the move...this shows H your dedication to the R/M and to him...so keep your focus on the positives...don't harp on him to cut contact because my H once told me that when I would bring OW up that would put the thoughts of her right back in his head...so let it be...he isn't seeing her...he is telling you that it isn't romantic exchanges they are having...so you need to trust him...the more you put trust in him...I think the more he will want to earn that trust...
Hang in there...piecing isn't easy...it takes more patience and understanding...but you can do it...