Same same I reckon. Neat glyphosate on cut stems knocks it back but doesnt kill it. Digging out and burning is about the only option. I cleared my place but now have a dozen outcrops. Birds shit the seeds out I think. Anyway not pleasant smoke can cause breathing problems. Horrid shit. There are other woody weed killers that work but that is nasty shit.
blackberries are rhizomal, so essentially have sectional root systems and will put down roots wherever the branch touches the ground, thus making them extremely hard to kill. using even high doses of Glypho wont kill off an entire mature plant, only a few "sections of it" thus why they resprout.
There's a few off the shelf blackberry sprays that work ok, but due to the waxy nature of the leaf most water based sprays lack penetration (as do I) but mixing them with kerosene will often do the job.
Commercial sprays do work but are expensive and will often poison the soil as well. There is no great solution to any of these noxious woody weeds other than persistence. In my gardening days we would simply cut and pull them out as best as possible, and treat the shoots as they appeared with a 3x recommeded dose of glypho and continue doing that for a year or two. works same for gorse etc.