house arrest

We are under house arrest due to the sleep habits of a certain one year old.  Every playgroup, library storytime, or mothers' group activity seems to occur at 10 or 10:30 in the morning, which is when Joseph takes his morning nap.  I mean, there isn't much I can predict about his sleep paterns (will he wake up at 4:30 am or 6:30 am?  will he want to have his afternoon nap at 1:00 or 3:00?) but I know for sure he's napping at 10:00.   Any efforts to game the system by putting him down at 8:00 in the morning or by acting extremely interesting so he won't be tired until 11ish fail utterly, and I'm left with a screaming, unhappy boy. 

Right now my plan is to find something to do around noon (like something involving other adult humans, which is complicated when you don't know anyone in your city, hence library story time, meetup.com, etc. and I have no control over when these activities take place), because he's almost always awake between noon and one.  This may involve rejiggering lunch so it takes place earlier or later (or more briefly) but I will try.