I've got about 10,000 JMB miles in my account. It is unlikely this will grow
into anything worthwhile in terms of flights.
I looked on the JMB web site but cannot find
a way to exchange these miles into another
program, be it airline, hotel, etc. Does
anyone have any strategy to suggest? Thanks!

You can redeem hotel stays for 10,000 miles.
Go to:
http://www.japanair.com/JMB/JMB_Awards/hotel.htm

Look in their hotel award chart to find a property that you would like and good luck.