Name, Conditions, and Pluralization of "Conscience' sake"

Solution 1:

I mention the phenomenon — or old habit, perhaps — of saying for conscience’ sake in this answer. You’ll also see the expression for righteousness’ sake in older religious works. A more common one is for goodness’ sake.

There’s no extra syllable in any of these, as the orthography indicates. In all these, the formulaic for X’ sake (where X ends in phonetic /s/), no extra syllable is pronounced to indicate the possessive. It’s just like how a plural already ending in -s takes no extra syllable to create the possessive.

this farmer’s field
these farmers’ fields

People also used to end their prayers by saying in Jesus’ name, Amen without an extra syllable, too, but for the most part, they no longer do so. Most (but not all) now say in Jesus’s name, Amen instead.

In answer to your question about a plural, conscience is generally construed to be a non-count noun, in which case it takes no plural inflection. If one did, however, its plural would have to be consciences, and the possessive of that is the same as the possessive of any other plural already ending in -s: just add an apostrophe without adding an extra syllable, so in their own consciences’ domains.