I value the DoI and the Constitution, but judgments based on them are not scriptural.
For what’s it is worth, when it comes to assessing something as sin, as abominations, we should neither add nor subtract from Scripture. This means dealing with the evidence we have from Scripture just as it is.
Now, it is said of divorcee that “God hates divorce” and that because of the hardness of their hearts that Moses permitted them to divorce.
But that isn’t all: for divorce is regulated. This is important because it indicates a class of objects between “abominations” and things that are just okay. These are things that are not good, which God may even hate, but which can be regulated and if properly regulated then the abuses of it are prevented. These are, just to be clear, NOT good things ... but neither are they automatically abominations.
Now, with respect to slavery we see that it is arguably also something that Moses permitted (because of the hardness of their hearts) but was told to regulate. This is the proper response to those folks who go on about slavery being approved of in the Bible because you do not regulate things that are harmless and not prone to abuses (their rhetoric point is demonstratably false).
So slavery apart from any other consideration is not, as you say, inherently an abomination.
Since we don’t have a clear statement where “God hates slavery” we cannot say it is to be automatically considered as bad a divorce is (divorce represents a betrayal of convenient relationship).
But it must be properly regulated, and Scripture has something to say about what constitutes that (or do you think Paul inherently treated Onesimus poorly in sending him back?).
If is here, that black chattel slavery was not just unregulated but was regulated is ways entirely at odds with what Scripture commends, malregulated if you will, that said system could be said to constitute an abomination.
But no person was engaging in sin just because they owned a slave and the government malregulated the estate if they did obeyed better commands rather than cultural/political ones.
Whereas homosexuality (or adultery for that matter) CANNOT be regulated to limit its evil ... nor can murders be. These are always worse.
If that put me at odds with this culture, well, I’m okay with that. We are not called to be approved of by society or even to care about its judgments.
“Covenant relationship” ... some typoes and autocorrects brought on by touch screen typing and pudgy fingers are just plain worse than others ...