Your argument has several fundamental weaknesses:
I don’t see that other stories are being excluded or slavery being “shoehorned” into “every situation” the last time I went to an NT property where a link with slavery was mentioned there weee also materials about servants, local miners on land owned by the estate etc.
It makes no sense to argue that because modern slavery exists we should not highlight it in the past.
If you don’t understand slavery (and the colonialism, and economic activity it helped facilitate) and its ongoing legacy today you don’t understand modern history.
Yes, transatlantic slavery does get more attention than some other topics you mention, because a) the huge numbers involved b) the profound impact on large chunks of the world - the Americas, Africa, Europe c) the ongoing injustice experienced by black people as a consequence of the ideas, ideologies, behaviours and representations that were borne from the trade and continue to influence many white peoples perception of and treatment of black people today.
You seem to have a real problem with your perception “all this slavery stuff” is an import from America. When you consider Britain shipped 3.1 million people across the Atlantic, why on earth wouldn’t it be an important topic in our history?