Forced Parameterization and CASE statements
So I should have done some more digging before I posted this. The restriction is explained deep down on this page: 
Forced Parameterization | Microsoft Docs

Specifically, this section:


  The &lt;select_list&gt; of any SELECT statement. This includes SELECT lists of subqueries and SELECT lists inside INSERT statements.


This tells me it's not specifically the CASE, but that I have included literals in the SELECT list.

Still, if anyone has any suggestions for working around this, I'd be interested.