Zeddy, I think a double pram at rush hour probably isn't a good bet, but if you can get on the first car of the train and are willing to go right at 5:00 or a little before, it's doable. People might stare daggers at you, but whatever.
Ches, a single would be fine, esp. if you get on the first car. I'd be happy to help you guys navigate if needed -- Zeddy, I'll probably be going the same way as you (for a while anyway).
For those who haven't been before, the Constitution Ave entrance is the one you want if you have a stroller (the "front" entrance, on the Mall, has stairs). Natural History is the building with the big dome on top. There's a big elephant under the dome that makes a great meeting place, so let's meet there.
This is gonna be really cool.