Let's reverse the order of the clauses, and punctuate a little differently, and show where there's been a reduction or an ellipsis:
She’s sure they could love each other again if he would just say
(that) he spoke too hastily, that of course he loves her and wants to
make it work, that they’ve had things stacked against them—he knows
that—(that) it’s been hard for both of them, and (that) they have to
somehow help each other, (have to) try harder to be content together.
There's no need for then when the main clause begins such a sentence, and it isn't really required in the original either:
If he would just say (that) he spoke too hastily, that of course he
loves her and wants to make it work, that they’ve had things stacked
against them—he knows that—(that) it’s been hard for both of them, and
(that) they have to somehow help each other, (have to) try harder to be
content together, she’s sure they could love each other again.
Of course, putting those that's back in to show the parallelism of the clauses ends up making the passage seem more "measured" or slow-paced, when it is actually a little erratic and emotional.