I would assert that the driving forces pushing the US Navy's interwar planning were not primarily a result of its experience in World War I, though that played a role. I would suggest that more substantial factors were the Washington Naval Treaty in 1922 (and its successors), the Great Depression, the Navy's annual "Fleet Problems," and a series of bills to expand the US Navy passed by Congress from 1934-40. This is a big, complicated question that could perhaps benefit from experts on diplomacy, naval architecture, economics, and the US Congress in the late 1930s. Hopefully someone else can chime in and provide more detail.

First of all, the Washington Naval Treaty placed limits on the number of warships that could be built, especially battleships, and their size and armament. The initial Washington Naval Treaty, negotiated in late 1921-early 1922, limited battleships and battlecruisers to 35,000 tons and provided tonnage limits for the participating nations. Quoting directly from Article IV:

The total capital ship replacement tonnage of each of the Contracting Powers shall not exceed in standard displacement, for the United States 525,000 tons (533,400 metric tons) ; for the British Empire 525,000 tons (533,400 metric tons); for France 175,000 tons (177,800 metric tons); for Italy 175,000 tons (177,800 metric tons); for Japan 315,000 tons (320,040 metric tons).

To meet these parameters, the US Navy agreed to cancel construction of the USS Washington and 6 South Dakota-class battleships in varying early stages of construction. The treaty also placed limits on the size of aircraft carriers and tonnage of carriers allowed, along with limits on the size of cruisers (10,000 tons, 8-inch guns) that could be built. The London Treaty, negotiated in 1930, prescribed the total tonnage limit of smaller ships. Japan negotiated slightly better terms here, getting 70% of what the USN and RN were allowed rather than the 60% negotiated for battleships in the Washington Treaty.

Combined with these diplomatic treaties, the Great Depression, which began in 1929, arrested much appetite for building out a large navy. There were other priorities for government spending for much of the 1930s. The vast majority of the battleships that the US Navy entered World War II with were older types that had been in service since before the Washington Treaty was agreed upon.

The first naval expansion act of the 1930s was the Vinson-Trammel Act of 1934, which finally authorized the US Navy to build up to its limits under the treaties. The 1934 bill also authorized the first new battleships to be built since the cancellations under the London Treaty; these became USS North Carolina and USS Washington (it takes a long time to build a battleship). There were further naval construction bills passed by Congress in 1936, 1938 and 1940. You asked in your original post whether "someone young and new wrote the right papers." It was a US Representative from Georgia named Carl Vinson who pushed for many of these bills to expand the navy. Today, a Nimitz-class aircraft carrier bears his name.

The 1940 bill was the truly big one, however. It is usually referred to as the "Vinson-Walsh Act" or the "Two-Ocean Navy Act," because it was intended to build a US Navy that would deter war in both the Atlantic and Pacific, or fight and win the war if necessary. These pre-war shipbuilding plans were remarkable in how prescient they were in foreseeing the needs of the US Navy during World War II. There were some whiffs -- construction began on two more Iowa-class battleships that were never completed, and the 1940 bill included Montana-class battleships that never came close to fruition. But crucially, the plan included significant numbers of Essex-class aircraft carriers, which became the backbone of the US Navy (especially in the Pacific) during the war.

Many of these decisions were informed by the Navy's interwar "Fleet Problems," large-scale annual exercises that were carried out with dozens of ships at various locations. Albert Nofi's book "To Train the Fleet for War: The U.S. Navy Fleet Problems, 1923-1940" has an overview of the situations for each of the Fleet Problems and the lessons learned from them. Admirals could test and prove concepts like how effective carrier-based scout planes were compared to using destroyers or submarines as scouts, whether seaplanes like the PBY Catalina were viable as torpedo attack planes, and other issues. The Fleet Problems weren't perfect; some lessons could only be proved in combat, and bureaucratic inertia and infighting was still an issue when naval aviators and gunnery officers butted heads. But the modern US Navy still considers the interwar Fleet Problems to be an excellent example of wargaming both for training and testing new concepts; the navy was in much better shape because of its annual Fleet Problems.

The experience of Germany's U-boat campaign in World War I certainly loomed large in how the US Navy fought World War II. It was apparent that convoys with escorting warships was the best way to defend against U-boat attacks. Even with this knowledge, the Americans and British still had to relearn some hard lessons. The advancements in sonar gave them some undue confidence that submarines could be found and destroyed easily. Some faster merchant ships were authorized to sail alone in the early days of the Battle of the Atlantic, until it became painfully clear they were still vulnerable to U-boats and were also included in convoys. But this does seem to be an area where the Allies "refought" World War I, eventually with better weapons and tactics to counter German improvements.

Like I said, this is a broad topic, and I hope some specialists with more knowledge about each of these areas can contribute and flesh this out some more. In particular, the construction of the North Carolina and South Dakota classes is interesting, because naval architects had to find a way to squeeze every ounce of armor, weaponry, and performance out of a 35,000-ton battleship (the limit got fudged a bit), but I'm not an expert on that. I'd suggest reading up on the Washington and London treaties (the negotiations and codebreaking are fascinating if you're into diplomacy), the 1930s and 1940 naval bills, and the Fleet Problems. You'll find fingerprints from each of those that informed the Navy that the US built and fought with during World War II.