>>2719967Lots of people suggesting the use of tractors, which you've already ruled out. My recommendation is a sickle bar attachment on a pole pruner. Pic related.
Let's you keep your distance from the pokey shit and also cut a good swath through. When you have it all on the ground you can pile and burn then use a weed wacker with a metal blade attachment to take all the surviving vines down to ground level.
For chemical control you'll need to mix something into your roundup. Crossbow or similar works well. Roundup is a medium duty herbicide, it will kill the leaves not the woody vine. Crossbow is specifically for fibrous plants, like fruit tree stumps, or wood fiber vines, just like blackberries. If you're feeling especially earth rapey, add a little diesel to your mix. It will help with keeping the chemicals on the plant and also with uptake in the cells.