> Since we're already using XHTML 1.0 Strict (albeit sent as text/html),
> and our CSS works, could it be that it's only when sending XHTML as
> application/xhtml+xml that this case-sensitivity is encountered?
Common misconception. It does not help that people form an opinion on this matter and become emotionally invested without doing some independent scrutiny of the W3C publications. It is because of this that there is a good deal of incorrect information about this subject online. The root cause of this confusion is actually the W3C, though, since this is stated but not in any matter that is prominent.
According to the standards XHTML 1.0 is intended to be a transitional technology between SGML and XML even though this is not explicitly stated. Knowledge of intentions in complex standards must never be presumed. I do mean all of XHTML 1.0 in intended to be transitional. The standards go further to describe degrees of flexibility by supporting three doctypes to represent the amount of toleration in reaching accuracy towards the XHTML vocabulary and syntax changes. The first of the two links above state in the XHTML 1.0 specification that documents may be labeled with the type "text/html". This means that sending XHTML 1.0 strict as text/html is valid in accordance with the XHTML 1.0 specification.
In order to create a flavor of (x)HTML that is not transitional and not open to confusion the W3C created XHTML 1.1. XHTML 1.1 is the only finished specification of HTML that requires the use of an XML related mime type: application/xhtml+xml.
In the case of your use of CSS with HTML there is transparent processing variance that you mean not be accounting for. HTML has been pretty standard and its standard support has been pretty universal since before IE6, possibly before IE5, and in these late modern years CSS processing is pretty standard across the board as well.
In summary don't expect things that pass through the DOM to reflect any level of accreditation or standards compliance conduct and flavors of XHTML 1.0 can be sent correctly as text/html.