.. Any green fingered experts here know what the chances of the privet regrowing at the bottom are?
Very high, 2 years ago I butchered mine back from 10 foot to 12″ stumps, they’re approaching 4 foot again and will need trimming this year. Only way you’ll kill them is by pulling the roots up.
Move on, your stressing over bushes, you must have something more important to do/worry about.