I have a few questions....
What level of contact do you have now in your semi-open status? And what level of contact do you expect to have once the adoption is opened? This probably needs to be spelled out, and may make dh more comfortable with opening the adoption early.
We adopted 2 girls (both privately), and the situations with their birthfamilies are a bit different, although they are both (I think) considered open adoptions. We met both sets of bfamilies when our daughters were born, but have not seen either since. DD#1's bfamily was in California, and by law, CA is an open adoption state. The bfamily knows our last name, address, phone number, etc. We know how to get in touch with them as well. We send pictures several times a year, and email more frequently. They (bmom and bgrandma) send Christmas gifts to both girls and bday gifts to their bdaughter/bgranddaughter. We just sent a gift to the bmom for the 1st time.
With our 2nd daughter (born in another state as well, but not CA), we got a post office box in another town so they can send stuff to us if they want to (hasn't happened yet but they said they were going to put a photo album together for dd). They don't know our last name or address (I think!). We know how to get in touch with them and send pictures/updates several times a year as well as more frequent emails. When dd was born, they asked what level of contact we had with our older daughter's bfamily and wanted to do the same regarding gifts, etc so that dd wouldn't be treated differently, but unfortunately this hasn't happened yet. She's still too young (not quite 2) to realize it, but she will soon enough.
In either case, if we had medical questions, etc. we could ask them.