Recent research (see below) indicates that conjoined twins are not
formed by the arrested fission of monozygotic twins, but rather by the
re-fusion of already separated monozygotic twins.

My question:  how late into a human pregnancy can this re-fusion
occur?  That is, what is the latest that a pregnancy that seems to be
going normally toward producing separate identical twins can end up
producing fused conjoined twins?

As a reference, here's the study that said re-fusion is in fact how
conjoined twins are formed (note Dr. Spencer is now retired, but a
Google search showed that she had impeccable credentials):

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From:  Clinical Anatomy (Volume 13, Issue 1 , Pages 36 - 53, year 2000)

Title:  "Theoretical and analytical embryology of conjoined twins:
Part I: Embryogenesis"

by Rowena Spencer *
Louisiana State University School of Medicine and Tulane University
School of Medicine, New Orleans, Louisiana

Abstract

A review of over 1,800 publications concerning the embryology and
pathologic anatomy of conjoined twins provides convincing evidence
that they all result from the secondary union of two originally
separate monovular embryonic discs. This fusion theory seems to be
confirmed by the adjustments to union and the pattern and incidence of
specific anomalies at the proposed sites of conjunction in more than
1,200 cases, all of which can be arranged in two uninterrupted series
of cases, the one united dorsally (in the neural tube) and the other,
ventrally (over a shared a yolk sac). No theoretical fission of the
vertebrate embryo at any stage of development, in any plane, in any
direction can explain (1) the selection of the observed sites of
fusion, (2) the details of the union, or (3) the limitation to the
specific areas in which the twins are found to be joined.

Your reference says that it occurs between monovular [each with their
own egg] embryonic discs. That is the stage of growth of the fetus
where they are two or three cellular layers 'thick'. They progress
beyound that by the 15th day.