That's a pretty valid theory.
But on the other hand, the Nova class and Intrepid-class are contemporaries, so can we really assume that the upgraded Nova as improvements that we don't see that take to at least Intrepid-class equivalent or better? I've give you tactically... we have on-screen evidence for that... but scientific and diplomatic? That's pure speculation and the observed trend if anything implies the opposite (the Connie might not have been the biggest, but even with DSC's retcons it's still the very desirable and capable "one in a million" assignment that it was before, whereas the similarly sized Intrepid now approaches the "runt" of the explicitly multi-role crowd in it's era).
The upgrades would have to be far more extensive if the Nova was able to engage and subdue two Negh'Var Klingon battleships. And while I know they didn't offer much in the way of resistance (at least from on-screen data), Harry had to be somewhat confident that his upgraded Nova would be able to take on those 2 ships.
37 years is nearly 4 decades... it would be impossible that the Nova was only brought up to Intrepid class level... the firepower to penetrate those shields and disable those battleships in a quick succession had to be far greater from Intrepid's baselines (also considering this is the future in which Starfleet was seemingly confident enough they can keep the Borg at bay too).
Like I said, the Intrepid class was a downsized galaxy class and was built less than a decade after it. The Nova class would start as initially inferior to the Intrepid and Galaxy class but would soon result in a modern starship with modern upgrades that would pretty much bring it on par with most ships.
Think USS Lakota... ala 24th century style. The rate of improvements would accelerate further, so for all we know, SF could probably reduce the size of most of their hw while improving efficiency and power outputs to the point where size as we know it becomes less and less relevant.