It could hardly have made that worse though, could it? The silence was a major issue. Many more people would have respected her effort to step in even if it didn't convince everyone.
It could've made things worse, yes, it's quite possible it would've been seen as too little and disrespectful, and we really don't know whether 'many people' would've respected it or not. Another possibility is that it would've fanned the flames, and that nothing short of her presence in London to appease the hysteria would've been accepted.
I mean sure, she could've done it, but beyond that we're all getting into the realms of speculation. Which is why it's better focus on what we do know, which is that the desire to remain at Balmoral with her bereaved grandchildren was a legitimate and sensible one, and unlike some other things she's done actually speaks well of her moral compass.
Yes there was hysteria drummed up by the press but I think there was also genuine anger stemming from the fact that the public could sense that the RF's response to Diana's death was not as wholehearted as it could have been. BP had historically been reluctant to acknowledge Diana's popularity. They initially thought that a private family funeral would be adequate which was ridiculous frankly given the level of public interest. And it was reported that PC had a fight on his hands to acquire a plane to fly he remains home. All these things built on the context of the stripping of the HRH title and her ostracisation when she was alive.
The anger was absolutely genuine, yes. I remember it well. This and the other poor decision making you mention don't affect the point that the queen wanting to remain at Balmoral was the right choice, and that her grandchildren should've been the priority.