Now, from what you say below, the ambiguity that your system currently enjoys may be (nomen omen) a blessing. That, in turn, can be taken as an argument for the minimalistic solution that I have suggested: don't go for a different markup mechanism, just use a different (non-TEI) namespace for the @altid.

Well, at this point I think that the adoption of TEI @corresp (with all its ambiguities and limits as pointed out by Lou) would be as minimalistic as the the inclusion of the foreign @altid, without the complication of modifying the schema and adding all the namespace stuff. In a sense, it would even be a more correct way to go in a (informal) semantic sense, since @altid seems to connotate a sort of alternate identifier of the local element (kind of a contradiction IMHO, since an ID should be unique at least in a given namespace) while its meaning in the context of Christian project (for what I can see) is that of a relationship of some kind with other textual segments.

So in the end I'd go with transforming @altid in @tei.corresp, which is moreover present in most of the elements.

My one cent...