Alright, taking into consideration all of the above and what I've sketched so far, I've come up with a backstory for the class.
Following the Constitution class Enterprise's theft of a cloaking device from a Romulan vessel in 2268 (TOS: "The Enterprise Incident"), Starfleet made several unsuccessful attempts to integrate the technology with current Federation vessel design - the stolen cloaking device degraded to a non-working state within weeks. As the possibility of a war between a united Klingon/Romulan force and the Federation loomed (though, in reality, the relationship between the Romulan Star Empire and the Klingon Empire was as tense as ever), Starfleet's engineers determined that new battleships would be the quickest and most practical way to either discourage conflict or to be ready for it.
Shipwrights examined existing designs and how cloaked ships targeted Starfleet vessels, noting several design features of vessels that made them uniquely vulnerable: primary hulls, interhulls, pylons, and warp nacelles. In each case, they had thin areas that disruptor pulse based weaponry tended to punch through, severely compromising hull integrity. To resolve these issues, Starfleet Command authorized a design team to prototype a battleship that surpassed these issues.
Due to a rushed production, non-Humans had little involvement in the design process and many design changes were kept mostly structural. Besides the general reinforcement of the hull, modularity and redundancy were emphasized: Torpedoes were housed in an auxiliary pod to keep such large stores of antimatter away from the main body of the ship, the number of warp nacelles was doubled as they tended to get disabled in combat quickly, and the residential sections of the primary hull were fitted with large duranium plates to minimize crew casualties. In addition, the prototype featured a hull separation mechanism. Unlike later vessels, the prototype had a single secondary hull.
Dubbed the USS Proxima NX-2500, the prototype suffered severe plagues of system failures and glitches. The faults eventually were attributed to warp core fluctuations caused by overuse - four nacelles simply were too taxing. Several days were spent reconsidering the project when an assistant engineer proposed the idea of two warp cores functioning in tandem. Theoretical computer models contributed by a Vulcan Science Academy team affirmed the proposal and a new tandem secondary hull design was used in subsequent vessels.
