the smart money is on the Excelsior Transwarp project actually being successful, and leading to the Warp Scale recalibration
This is what I've always thought. More or less, "Transwarp" is just a word to mean "Faster than the Warp we have now", which would also be applicable to Borg Transwarp Conduits.
I've thought the "tell" was the line in "Flashback" on Voyager when Janeway said that ships of the 23rd century were half as fast as they were in the 2370s. We know from the Warp Scale recalibration, that's more or less true. As I see it there are distrinct generations of classes.
-Gen 1: The NX era, which lasted in improved forms until around 2200. This allowed Starfleet to explore in a few hundred light years time efficiently. But the Federation was still a pretty "loose" organization.
-Gen 2: The pre-Constitution era, from around 2200 to 2260. Lots of Discovery-era ships here. This didn't allow much more exploration, but the superior speed and homogenized tech and ship design allowed the Federation to become more formal.
-Gen 3: The Constitution-class era. This class, specifically the improved refit allowed for highly serialized and modular ship-building for the first time. Starfleet grew, the Federation grew. The Federation pushed into the Alpha Quadrant for the first time (before hand, it mostly stayed in the Beta Quadrant). The Miranda-class variants were hte main legacy of this era, as they proved the most expandable with a modular aft saucer section, and without the secondary hull. Constitutions appeared in the 2340s and 2350s, but did not replace older classes en masse until after the Fed-Klingon War. They were built based on the experiences of the Fed-Klingon War - rugged and durable. While the original constitutions were more firmly explorers, the refits and its derivatives had a form military design principle behind it, in case the Klingons attacked again. This era lasted roughly 40 years, around 2260-2300.
-Gen 4: The Excelsior-class era introduced a whole host of new technologies that would form the foundation of a series of technologies that would "make" the Federation and Starfleet in the 24th century. It took the modular design of the Constitution class and evolved it. The Transwarp engine more or less succeeded and ships became twice as fast, with later smaller versions being retrofitted into Miranda-class ships. The Federation started to explore and expand deep into the Alpha Quadrant until it came smack up against the Cardassian Empire, which led to a series of wars in the 2340s and 2350s. Gen 4 "shrunk' local space the way the 707 and 737 "shrunk" the world by allowing routine transit of the federation, and spin-off technologies wholly replacing Gen 2 and Gen 3, that by the 2370s, Miranda class ships had much more in common with Excelsior class ships on the inside than the Constitution class. Excelsior-class era ships typically share a common hull plating type and/or nacelle/secondary hull/saucer shape. This era was supposed to last roughly 40 years, but ended up lasting about 60, from around 2300 (when the Excelsiors started phasing in, and cruiser-type Constitutions out) to 2360.
-Gen 4.5: The Ambassador-class era of the 2330s/2340s was supposed to be another leap forward, on the scale of the Excelsior jump decades before, but the technologies weren't quite there yet. Instead, it modestly evolved Excelsior era tech and a new ship-building era was put off as improved Excelsiors were build instead.
-Gen 5: The Galaxy-class era. Because the Galaxy-class was supposed to meet and surpass the leap ahead that the Ambassador-class failed to meet, and was the most ambitious shipbuilding program in federation history, this era came in two steps.
The first step was in the late 2340s / early 2350s when the New Orleans-class, Cheyenne-class, Challenger-class, Niagara-class and Freedom-class entered service. This ships did not have large production runs, but replaced older Excelsiors and Mirandas. They combined developmental aspects of intended Galaxy-class technologies with proven components from the Excelsior, Ambassador and Miranda classes. To avoid a repeat of the failure of the Ambassador class and reduce desk risk, the technologies were spread out widely among these ships to gain operation knowledge of them before the Galaxy-class was built. They share with the Galaxy class, a new hull plating, aspects of a new saucer design and interior layout, and with some exceptions the new nacelles that would allow the Galaxy-class to explore further and faster.
The second step came in the late 2350s / early 2360s. With the design and technologies proven to Starfleet's satisfaction, Galaxy and Nebula class construction commenced. This would open up Starfleet to long term exploration (and expansion) on the other side of the Romulan Empire, Klingon Empire and Cardassian Empire. Instead of making more of the Gen 5 Step 1 series of ships, the Federation also started taking the successful Galaxy-class tech and putting it into a purpose-built design to operate nearer in Federation space and in time replace the improved Excelsiors as the workhorse. This was to be the Intrepid-class, but the Borg threat changed that. Starfleet finished out the Intrepid class program and did a limited production run, but they would not replace the Excelsiors.
-Gen 6: "The Federation Battlefleet-era" was the first era of ships not designed around exploration, but around an increasingly dangerous galaxy. Designed in the wake of the Borg threat, and then accelerated during the Federation-Dominion Cold War, Starfleet again abandoned long term exploration as it's sole interest in ship building and focused on a balance of military capability. Hull forms were more compact and sleeker. Armaments were much greater. The hull plating style of the Gen 5 era was abandoned in favor of some kind of armor. The ships were generally far more maneuverable. Many Gen 5 technologies (including late tech like bioneural circuitry) was incorporated and evolved, and paired with a modernized focus on military capability. The peace time experiment of families on ships was brought to an end. The ships of this era are the Sovereign class, the Akira-class, the Saber-class, the Steamrunner-class, the Norway-class, the Prometheus-class, and the Defiant-class. The Nova-class represented a bridge between Gen5 and Gen6. The results were quite clear: while Gen 4/4.5/6 got rolled at Wolf 359, Gen 6 destroyed the Borg Cube in the Battle of Sector 001 with modest losses. The post-Dominion War / post-Endgame Luna-class represents an evolved Gen 6 design shifting back to a long term exploratory role.
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Basically, I think Ships got faster in spurts. There was substantial increase in speed between Gen 1 and Gen 3 over about 100 years. Then Gen 4 I think, basically doubled speed and allowed for the "big" Federation of the 24th century (versus the "small" Federation of the TOS Movie era). Gen 4 and 4.5 were basically the same for speed. Gen 5 allowed for a real increases again, but only on Galaxy, Nebula and Intrepid classes and it wasn't as big of a leap above modernized Excelsiors except at the very upper end that the ships rarely traveled at. Gen 6 did nothing to increase speed (but greatly increased maneuverability and other aspects of ship design).
So what's the next step? If I were a show writer, I'd make the biggest legacy from Voyager's 7 years in the Delta Quadrant be Quantum Slipstream. I see it as "the answer" to how to get Federation ships around faster. The Trek Literature universe handled it right. It's a very-federation compatible tech that can co-exist with Warp Drive and Starfleet ship design. If the Constitutions made getting across Sectors pretty fast and routine, and the Excelsiors made getting around known local-space pretty fast and routine, I'd like to think that Quantum Slipstream would open up the entire galaxy, truly, for the first time. The Federation one day would need something new for intergalactic travel, and sure Transwarp conduits can provide short cuts. But I think it's a fitting story that after a good central of modest (but meaningful) improvement, that the Federation had to have a ship be pulled 70,000 light years away to discover the means to taking that huge jump forward.
