Single listener for multiple Oracle homes?
Question: Is it problematic to use a single listener for multiple
  Oracle homes?


No.  There really is no valid reason to run multiple Listeners.

You just need to make sure each database "registers" with that one Listener.


  I get that it's a single point of failure, but is there
  also a performance hit?


I'd be more concern with your single node databases being a "single point of failure" before I worry about the Listener as a "single point of failure".


  Something else I'm not thinking of?



K.I.S.S.:  Just use a single Listener.
The Listener does not have to be on the same server as the database
I believe you can use Oracle Grid to run a collection of Listeners.



  Question: Is there some other way I can run a listener out of each of
  the new Oracle homes using the same port? Again, we're not using
  virtual IPs, so I'm stuck with new host "foonew" + port 1521.


No.  This is an OS thing, not a Listener thing.