Our lovely Hedge is laced with brambles. I cannot access their roots. What is the ideal tool / product to perhaps inject.
I managed to kill a weedy vine in a similar situation by cutting the vine close to the base and using a paintbrush to apply roundup to the wound. I made the cut on an angle to allow a larger surface area and then painted it onto and new leaves as the side shoots popped up. Foliar spray the hedge at the same time so the hedge is healthy and strong and outgrow the brambles.
It frequently happens in hedges that tip rooting brambles will get started in dense growth and hop from one protected location to another making control very difficult. The weakness of this growth pattern lies in the fact that the roots are always thinner than the majority of the hedge roots. The issue is getting at the bramble crowns. If you could sever the them from their roots then they would dry up and go away. The problem is getting at the crown to sever the roots.
There is a tool for digging dandelion roots which has a sharp Y type tip whose purpose is to sever a soft root. Mostly designed on short handles for hand digging, while it might sever bramble roots you can't get close enough in the hedge to allow it to work. Say you take a one inch diameter steel pipe about six feet long and fashion one end into a sharp Y - this would allow access to the bramble root (they will be at the surface) and the mass of the pipe will give enough heft to break roots from a distance. You will be working somewhat blind but most of the hedge roots will be much deeper than you need to access.
Hedges often have a sunny leafy side and a shady not so leafy side. Working from both sides you could sever many bramble roots without need for chemicals. Likely you will need to make this an annual task but it will significantly reduce the inconvenience of snagging bramble shoots.