How could Britain go about getting its American colonies back?

The answer to your question may be to think about how the British could have avoided the Revolutionary War and American independence to begin with. Once the Treaty of Paris was signed on September 3, 1783, formally ending the war, there was little Britain could do to reclaim colonial status for the American colonies. Emboldened by the defeat of Great Britain, a significant world power, and excited by the prospect of self-governance, it is highly unlikely the American colonists would see any need for remaining colonial citizens of Great Britain. Suppose for a moment that, rather than go to war, Great Britain had conceded to the demands put forth in the Declaration of Independence. Would that be enough for American colonists to remain as colonial citizens?
The list of grievances from the Americans against the King of Great Britain is outlined by this statement in the second paragraph of the Declaration of Independence:

The history of the present King of Great Britain is a history of repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States.

The colonists believed there was a long pattern of abuse by the British, and the only remedy left after long-suffering forms of disrespect and indignity was to break from Great Britain's colonial rule. The Declaration of Independence says,

To prove this, let Facts be submitted to a candid world.

From this point forward in the document, the writers begin to list the facts and reasons for American discontent with Great Britain. By reading the list of complaints of the American colonists presented in the Declaration of Independence, it becomes clear that the damage to the relationship between the colonists and Great Britain was substantial, and likely beyond repair.
The only conceivable way in which the colonies would return to Great Britain is if they had conceded on every issue as stated by the Declaration of Independence. More than likely, this still would fall short, as even in concession Great Britain would be admitting they were guilty of the abuses that had transpired previously. The American colonists would be encouraged by forcing Great Britain to change the governance structure of the colonies. Eventually, both parties would recognize the decline of Great Britain as a world power and the rise of America to assume the void left by the absence of Great Britain on the world stage.
https://allthingsliberty.com/2013/09/american-independence-inevitable/

https://www.archives.gov/founding-docs/declaration-transcript

https://www.smithsonianmag.com/history/myths-of-the-american-revolution-10941835/