Himalayan blackberries the OP mentions (from europe) are in a world by themselves in the Pacific Northwest where they grow like crazy. I am in the same area as the OP. Our native blackberries are a nuisance. Himalayan berries are a nightmare.
And all down the Pacific coast! Years ago these apple orchard terraces were sprayed with herbicide to keep down the blackberries. About 1970 Dad had to find a different contractor to till, spray, harvest this little orchard. After that, areas that were too steep to cross-disc weren't maintained. Minor infestations of blackberry quickly became impenetrable jungle.
In 2005 I tried ripping out blackberries with the backhoe to restore access along one terrace down in back, and found the apple trees had grown in grotesque directions to reach out of the jungle to reach daylight. There wasn't much apple production there, so I haven't tried to maintain it since then. That row disappeared into jungle again, and we get more berries there than we need for making jam - several dozen jars each year. This weekend relatives will be visiting to pick all they want.
Pro tip for berrypicking: Glove on left hand to pull clusters out of the jungle to pick with right hand without reaching in and getting thorned. Also this tension prevents catapulting the rest of the cluster as you pick the first berry. Pick into a small bucket on your belt.
Is that correct Himalayan Blackberries from Europe? Either way what is the difference between them and native blackberries. I do not know what we have, I just know they are good!
Himalayan Blackberries have nasty thorns like a rosebush but at closer intervals and the tips break off in your skin if you can't gently move opposite the direction the thorn went in. Patience is essential. The berries are larger than native Blackberries. The Natives grow in the same place but are outnumbered by Himalayan. Native thorns are much finer and easier to avoid
Digging out blackberry roots is difficult because they go so deep. Car keys for size comparison.
Now that we're organic certified, discing is the only method used against Blackberrries and Oaks that spring up everywhere in the orchard. But this doesn't get the intruders that are so close to apple tree trunks that the disc can't get them. Every few years after the ground is saturated, I go out and rip out those too-close weeds that have roots tangled with the apple roots. Using the backhoe when a slender trenching shovel isn't sufficient. Oak roots pop out like carrots. Interconnected Blackberry roots aren't as easy, but tugging on the largest one generally brings up the rest. What got me going was the harvest contractor told me he spent $thousands trying to save the eye of one of his crew who was snagged by a Blackberry thorn while harvesting.
Overall the orchard is much cleaner that when I started this cleanup 20 years ago.