Strut Mount Gap symptoms - Would strut brace help?

I'm curious to know from the great experts that we have on this site about what the expected symptoms would be from the infamous strut mount gap. I've heard about clunking when accelerating or braking, but could a high speed vibration (like this one) be the result of this issue?

When I last replaced my front struts, I also replaced the strut mounts. However, I made the silly, but (as I've read) occasional mistake of using the wrong nut to secure the spring to the strut and mount. It didn't take me too long to figure this out and correct my mistake. But after I got the right nuts in the right locations, I still had this strut mount gap, even with essentially new struts and mounts.

I'm wondering if this could be the source of the vibration that I've tried so long to diagnose and correct. (That is, could the top of the struts be wandering since they are essentially not held tightly in place?) And if so, would the addition of a strut brace help to mitigate this issue? Or is that a solution to a different problem?

For those who have replaced their strut mounts, does anyone have a spec for how tall they should be to work properly?