Kolchin's discussion of the contested meaning of freedom is not, by itself, the evidence you need for your specific proposition that racial equality was socially constructed and that emancipation did not immediately make formerly enslaved Black people socially equal.

Those are related questions, but they are not the same question.

For your specific proposition, I would use a combination like this:

Historical evidence

Giuliana Perrone (2019) is particularly useful because she directly examines what happened to the social and legal legacies of slavery after abolition. She argues that abolition was a long and complex process and that the legacy of slavery continued to affect former slaves' lives despite changes in positive law.

Historical institutional evidence

The Library of Congress documents the persistence of hostility, segregation, racial violence, and restrictions on formerly enslaved African Americans after emancipation.

Conceptual framework

Rogers M. Smith (2022) gives you the distinction between legal citizenship and lived citizenship, the latter involving social standing and recognition as civic equals.

That combination is much closer to your actual argument than trying to force Kolchin's “contested freedom” discussion into it.

A concise author-first formulation could therefore be:

Giuliana Perrone (2019) argues that the abolition of slavery was a long and complex process because changing positive law could not by itself erase the legal and social legacies of slavery that continued to shape the lives of formerly enslaved people.

And for the broader conceptual distinction:

Rogers M. Smith (2022) distinguishes legal citizenship, understood in terms of equal legal rights and duties, from lived citizenship, which requires sufficient social, political, and economic standing for people to be recognized as civic equals.

This, I think, is the missing scholarly foundation for the fourth dimension you want to add to your Cambridge argument. It lets you say something more precise than “equality was only on paper”: emancipation changed the legal status of formerly enslaved people, but the pre-existing social hierarchy did not disappear merely because the law changed.