How to have Siri pick from the list s/he just read to me?
"I am looking for an answer other than choosing unique types (eg, setting one of his cell numbers to "pager" instead.)"

then I have no answer ;-) 

Change the type &amp; you can just say the type, cell [US] mobile [UK], office, home, etc. 

You don't even have to wait for the list, you can just say to Siri, "Call Fred, cell."
 So long as there's only one Fred &amp; one cell number listed for him.

If there are 2 Freds, then "Call Fred Smith"; 2 cells, then differentiate 'work cell' or 'cell 2' etc