It's not clear from the letter that the OP actually wants an open relationship. Rather, it sounds as though he was lashing out after focusing on porn and masturbation fantasies ("During that time, I thought a lot about other women, mostly as novelty, although I never crossed any lines." --Apart from the emotional affair possibility, which the advisors don't touch on.)
He must work hard on building trust back, yes, and I think that the next thing he says after his apology should be that he wants to go into marriage counseling solo and with her to improve their communication. In daily life, he needs to 110% visibly commit himself to their family and start centering his thoughts and emotions on his real, present wife. However---when the letter was written, it had already been "several weeks" and this situation does not improve with time. His wife has had that time to think about it, to consider the possibility of life without him, and to look for advice of her own.
no subject
He must work hard on building trust back, yes, and I think that the next thing he says after his apology should be that he wants to go into marriage counseling solo and with her to improve their communication. In daily life, he needs to 110% visibly commit himself to their family and start centering his thoughts and emotions on his real, present wife. However---when the letter was written, it had already been "several weeks" and this situation does not improve with time. His wife has had that time to think about it, to consider the possibility of life without him, and to look for advice of her own.