My HF antenna is a Beam, not a vertical.
Sorry, I should have better articulated that.

The 6 band HF beam is 1' above the thrust bearing, and ~ 8' above the beam
is the triband vertical (at the very top of the mast.)
That said, there will definitely be a significant RF field above and below
the beam, as well as to the obvious front and back of the beam.

So, is there a danger of inducing destructive voltages to the vertical
above? What about other antennas on my roof near the tower?

My beam is well above the roof line, but as I have two tripods on the roof,
each with assorted verticals and beams {6m - 70cm LogP, two discones, a 902
yagi, and 902 vertical, and a 220MHz vertical.) These are each 25 to 30
feet away from the HF beam. There's also a distorted G5RV (aka: has a 90
degree turn near the end of the long leg as to stay on the property) running
off the roof to some trees along the back fence.

So you see my concern about having a 1KW RF source in proximity to all the
other antennas.

'73, VE3PMK