Update: I replaced the code using XML::Simple with XML::Parser and the problem went away. This doesn't prove that the problem isn't ultimately caused by (the verion of) XML::Parser, but at least in my case it required the interaction of XML::Simple to make the POSTed variables not show up.

As a side note, while I was initially satisfied with XML::Simple, I soon found that coding the handlers for XML::Parser was no more trouble than using XML::Simple ... at least if you have the case where you may have 0, 1, >1 of a tag type. Cuz then you've gotta start telling XML::Simple about array folding, key tag lists, etc.