That was the one thing Britain really did not need much help with, they already had a navy twice as big as the next two combined together.
You do not understand the Battle of the Atlantic and the issues it caused being based entirely on the ability to replace merchant shipping hulls rapidly. Indeed, by their own estimates the RN actually should have
lost the Battle of the Atlantic by losing more than 500,000 GRT of merchant shipping. And not once, but twice. (They did not factor, and neither did the Germans, that the actual bar on the high jump was at 1.7 million to beat the US and its production capabilities.)
You do not understand the size, age, constraints on, and function of the Royal Navy during WW2. (Not as large as that, too old, unable to deploy major assets at sea for long periods due to insufficient auxiliaries and unwillingness to replenish underway, what function? The Home Fleet wasted the entire war, and the RN as a whole didn't even realize the Atlantic was where the war was going to be fought until late 1943, after four years of war.)
Louisiana might not have been purchased but since Napoleon had it the British might well have conquered it.
You do not understand how the British based their diplomacy of the period on conquering things so they could use them as bargaining chips for the following peace. Louisiana would have been returned in the peace because they would have had no interest in allowing it to develop.
Arguing what-ifs with any kind of certainty is ridiculous. Chaos theory is laughing at all of you. 
Ah, but I'm not arguing what-ifs.

I have actual evidence for all my positions.
