I'm looking for a home office telephone that will route calls to
different answering machine mailboxes based on incoming "Distinctive
Rings."

I have single line phone service into the home. 
I added Verizon's SmartRing (Distinctive Ring) service. Calls to this
second number come through our single line but with a distinctive
ring.

There are stand-alone switches called call processors, call routers,
call directors, or sometimes line sharing devices -- that will route
calls to different ports based on distinctive ring:
http://www.command-comm.com/telephone_line_sharing.html

I'm looking for a stand-alone product that contains all these features
-- phone, digital answering machine (with at least 2 mailboxes), and
distinctive ring switch.

Thanks in advance for your help.