Never mind, soon after posting this, I decided to compare the .vcxproj file for my "real" Makefile project with the file generated in my experiment forcing "/TP" for a Visual Studio-created console project.
It turns out that if I include the setting in my Makefile project, Visual Assist now behaves as expected!
<ItemDefinitionGroup>
<ClCompile>
<CompileAs>CompileAsCpp</CompileAs>
</ClCompile>
</ItemDefinitionGroup>
Maybe this will be useful to someone else.