At any point between the Treaty of Paris and the War of 1812, was there ever serious thought in Britain put towards either taking the Colonies back, or at least fighting a war with the new United States?
There was absolutely serious thought about fighting a war against the United States again. The thought was "don't."
Owing to the French Revolution, which kicked off six years after the end of the War of Independence, Britain was much more concerned with continental matters. In 1793, the new regime in France declared war on Great Britain which lasted, with a couple of breaks, until 1815.
War in North America was expensive, difficult, and over all not worth much. Britain had no interest in retaking the colonies, apart from some braggadocio from officers involved in the War of 1812. At a state level it was never a goal.
For instance. In the 1790s, the United States was involved in the Northwest Indian War, which to make a complicated story simple, was backed by British Indian agents, who made certain promises regarding continued support. Following the Battle of Fallen Timbers, the retreating native forced regrouped by a nearby British fort, and requested entry. The British refused, reneging on their promises of support. This, more than the loss at Fallen Timbers, broke up the confederacy and won the US the war.
The confrontation at Fort Miami was tense. The British had to put up with Wayne's bullying, even though the likelihood of a successful American siege of the fort, owing to short supplies, flagging morale, and other concerns, was low, the British could not risk a shooting war with the United States while they were fighting a war against France at the same time.
The same concerns dominated British thinking during the lead-up to the War of 1812. Of the three grievances listed in Madison's declaration of war, the British gave in on one, repealing the Orders in Council that restricted American trade to Europe.
To my knowledge, the British government never seriously considered an effort to reconquer the colonies, owing to bigger problems on their own doorstep.
For more detail on the Fort Miami confrontation, which I've only very briefly described, check out Bayonets in the Wilderness by Alan Gaff, which covers Anthony Wayne's efforts in the Old Northwest.
For a decent overview of the British position during the War of 1812 and before, I'd recommend Jon Latimer, 1812: The War with America which situates the War of 1812 in the global sense better than any of the monographs written by Canadian or American historians.