While @Dave's response made sense, it didn't actually work for me. But it did send me down the path of further investigation.
The biggest key was that in order send the list attribute/values pairs as a "post" in the "web form processing" sense, you need to do this:
Set the payload "type" to:
application/x-www-form-urlencoded
This forces all elements to be "post'ed". If you want a mix bag (which for reasons known only to purest is "bad form") then you need to jump through more hoops.
See the following link for details:
Mirth Forums Thread related to accessing a RESTful web service