Definitely not a answer, but too long for a comment, and just for completeness:

As pointed out by მამუკა ჯიბლაძე, Higgs writes in Injectivity in the Topos of Complete Heyting Algebra Valued Sets that this paper is related to the unpublished paper you are looking for (cited as [5] by Higgs):

An earlier version ( [5] ) of this paper was accepted for publication in
the Canadian Mathematical Bulletin but for various reasons I discontinued the process of seeing it through into print. In addition to the present
contents, [5] contained: a brief account of logic in $\mathcal L(\mathcal A)$; the Lawvere Tierney version (for $\mathcal L(\mathcal A)$) of the independence of the continuum
hypothesis [14]; a sketch of a proof that $\mathcal L(\mathcal A)$ is equivalent to the category
of sets within the universe $V^{\mathcal A}$ of $\mathcal A$-valued set theory; a mention of
sheaves on an arbitrary site from the point of view of $\mathcal A$-valued sets; and
some elementary remarks on boolean powers and ultrapowers in relation
to $\mathcal L(\mathcal A)$.

[5] D. Higgs A category approach to boolean valued set theory, preprint, University of Waterloo
(1973)

[14] M. Tierney, Sheaf theory and the continuum hypothesis, in Toposes, algebraic geometry and
logic (F. W. Lawvere, éd.), 13-42, Lecture Notes in Mathematics 274 (SpringerVerlag, Berlin, Heidelberg, New York, 1972).