BTW, you would have to do this observation-by-observation row/column
elimination and matrix inversion in the MI procedure, anyway. It is not
going to be blast fast, either. So unless StataCorp would want to
implement that as a core set of commands (yes, I know the concept is to
send everything off to ado-files, but this is a clear exception), the
admirers of the missing data routines might want to consider the
alternative software.
There is now a third way -- write a plug-in that does the job (as E.
Leuven and B. Sianesi recently did for their psmatch2, to speed up some
of its lengthier computations). That will (if written well) overcome
the speed issue.