Trackbar, slide all keys in front of Time Slider?

I'm looking for a tool which does this. Maybe it exists already but my search skills are too weak to find it.

This is a feature common in video editors, where if you select and drag a current clip (a keyframe in the Trackbar) to the right then it automatically slides all the other clips after this one to the right as well. Sometimes called Slip Mode.

Currently I have to zoom the Trackbar all the way out to the full animation length, select all my animated objects, drag-select in the Trackbar all the keys including my current time but not before, then drag them forwards in the Trackbar.

This for editing an animated camera in an architectural flythough, if that helps visualize what I'm doing, editing the speed of the camera in each room as I fly through a large building.

Instead I was hoping there's a tool that lets me toggle a mode, which when I drag a single key in the Trackbar, it drags all subsequent keys as well, on all animated objects. Toggling the mode again would revert to default behavior.

Thanks for any pointers or help!