I completely agree with your interpretation of events in both films and how they are incongruous with each other. In fact, I’ve argued for this point several times on these forums.
This isn’t to say that RO is a bad prequel due to this. The materially problematic events only happen at the very end of RO and could be changed via fanedit, leaving the rest of the film basically the same.
The bigger issue here is one of spirit. As you said, Vader is following on the trail of Rebel spies which stole the plans during a battle and lead to Leia and to her alone. She is the only link Vader has to the Rebellion, and this explains why he is so bold and ruthless in pursuing her across the galaxy.
Contrast this to RO, where Vader has captured an entire Rebel capital ship presumably with logs detailing many potential leads. The shadowy web of spies are instead enemy combatants brashly breaking into a military installation on a whim, initially with no greater support in the Rebellion. Where the opening of ANH could imply a victory long-planned by the Rebellion, it is instead a chaotic near-failure at every turn. Sure, it makes for a wild ride, but the word spies implies some level of professional subterfuge that simply doesn’t exist in RO. I would not consider any of the main crew of RO ‘spies’ except for perhaps the defecting pilot Bodhi Rook and even then his spying was coincidental and not premeditated. Perhaps Cassian Andor is more of a professional spy, but we never see this in action.
Furthermore, it is implied that the Rebel spies were operating under cover of a separate, perhaps diversionary, battle instead of a group of rogue combatants dragging the rest of the fleet into a desperate action. Of course there’s some amount of speculation here but if the brief original crawl specifies two distinct groups (spies and combatants in a battle), then I would expect these to actually be functionally distinct in the plot of the prequel.
Finally, to expand on your point that Leia had plausible deniability in the original, I would go further and say that Leia’s presence at the battle, combined with knowledge of a weapon which can destroy planets, heavily implies that the Organas knew full well that they were putting their planet in deadly peril. I cannot put into words how reckless this makes the Organas out to be in the context of ANH, and it takes away from the tragedy of Alderaan’s destruction knowing that their rulers acted knowing their hand could so easily be revealed.