This may not be of any help to your particular situation, but I thought I'd throw a few personal observances in here.
I'm the adult daughter of a widower who has just this year remarried. We lost my mom two years ago this month, and dad married "S" this summer, so not quite two years had passed. My parents were deeply and madly in love with each other for over 45 years when mom suddenly died, and I for one cannot be happier that my father has found love again. However, my older sister and brother are very antaganistic towards the whole thing, especially since our new-step mom is quite a few years younger than dad.
I think it's all hogwash. Both of these people are over 50 and as such are quite capable of making wise decisions with no help from their children. All of us kids are are fully grown with families of our own, and it just irks me to no end that my siblings are giving dad such a hard time about this.
I'm sure it helps that I adore my dad's new wife. My brother and his wife had one negative experience with this woman way a few years back and have based everything on that one experience. They won't have dinner with my dad and "S", which is just stupid. They did show up to the wedding reception but not the actual sealing. "S" has never been married and so she and my dad went ahead and got sealed. I'm totally fine with that too.
It may also help that I'm divorced and have actual real-world experience with the whole "ability to love more than one person" thing. That seems to be the thing my sister is most upset with. She thinks mom would be horrified that dad was sealed to another woman. I disagree there too, and have actually had confirmation in my hunches that mom helped pair "S" and my dad up together from up in heaven. She took such good care of him and I'm sure she wants him to continue to be taken care of down here. He's got years and years left of living, we're all sure. He'll probably outlive this second wife too! j/k
My kids (who are all teens) think that Grandpa's cool for having snagged him a "younger woman"!!!
Anyway, you're gonna have some family members give a hard time and some family members will embrace you, if he ever gets his head on straight. I have a feeling that your man is getting flak from his family and that's what is causing his reluctance to take things further. My dad worried about that too, but his friends (two of which are current bishops) and I kept encouraging him not to worry and to just go on and start enjoying life again. Ever since he started dating "S", he looks so youthful and exhuberant. I could not be happier for him.
I wish you luck.