New Video of Dad Rushing Daughter's Graduation Stage, Interview with Cops

The dad who rushed his daughter's graduation stage to keep her superintendent away seemed to be waiting for his moment to shine -- based on new video we got a hold of.

TMZ has obtained additional footage from Baraboo PD that shows the incident in question -- namely, the father of the high school girl who was ready to walk across the stage ... only for her dad to jump in and whisk away the superintendent, refusing to let him shake her hand.

We've seen this moment from one POV -- but now, in this new clip, we can see it from a bird's eye view ... capturing the entire ruckus from beginning to end with a wide angle.

Check it out ... you see the dad hanging out on the side, apparently keeping an eye out for when his kid will be called -- and once she enters the frame, you see him spring into action.

He runs up onto the stage and immediately goes for Superintendent Rainey Briggs -- shoving him away from the line of school officials and getting into a little bit of a shoving/shouting match with him.

You can tell Briggs is taken aback ... and the two men are eventually separated by others.

The cops ended up interviewing the dad here later that night ... and TMZ obtained that video as well. You can hear what he says when he's asked why he did what he did -- and it sounds like the dad says his daughter previously ran into some type trouble at the school.

Unclear what exactly he's referring to -- but whatever it is ... he seems to blame the superintendent for how it was handled ... and he grouses about how he doesn't like him.

As we reported ... Briggs ended up getting a temporary restraining order against this Papa Bear, and the father has also been charged with disorderly conduct as a result of all this.

Many suspected race was a factor, but from the looks of it ... there's no evidence of that.