That may have been because Picard had accepted the Probe by then (or at least was not resisting). If he'd truly been resisting the Probe and not accepted it, then it might've allowed them to terminate the contact.
Picard was "living" a year a minute, by the time they attempt to end the transmission Picard had (from his prospective) been in the program for years.
So I think it's safe to say he didn't hold any grudge about it.
I don't agree with your interpretation, Picard said that it was an important experience in his life, but where are you seeing forgiveness?
There's a very good chance that the wife, the children, the grandchildren were not based on real people, they were fictitious characters created for the program. Picard's "character" the same, not a real person. Picard must realize this.