I see this is an old conversation, but I have an answer to the problem! I had the same problem, cedar tree roots invading my raised beds. Here's what we did:
We dismantled the beds, put all the good top soil in garbage cans to use later.
We leveled the ground and covered it with 2 layers of commercial grade landscape fabric.
We bought metal raised bed kits (size of your choice) from https://www.metalgardenbeds.com
We placed 8x8x16" cinder blocks into a rectangle the size of the beds we chose, then put 8x2x16" pavers on top like cap stones. (photos were taken before we thought of using the cap stones). Place a row of the same blocks (minus the pavers) down the middle of the bed (to support the new floor/bottom).
Purchase some galvanized roofing panels. Use one of the galvanized metal sides as a pattern, and cut 2 more pieces for each bed.
Then assemble the beds: follow the instructions, but add the new sections to the bottom two bolts so the pieces extend into the "bottom"; mine overlapped, but they don't need to. Drill some drip holes, paint with paint made for galvanized metal. Once the whole bed is assembled, get some help and lift it onto the cinderblock base. I added hardware cloth strips to fill in where the new floor does not cover (under the supports between bins). Cover the bottom with a layer of garden fabric and fill with appropriate soil for raised bed containers.
Zoom in on the first photo to see how we attached the bottom. We originally built this bed 2-blocks high, but decided to lower it this year, so we emptied it and moved the bed off the blocks. The bottom was clear, no root invasion, and the bed bottom stayed intact. The beds do a great job, we had a bumper crop of kale, zucchini and cucumbers last year. They do get hot, so I will likely insulate the east side before I refill it. Hope this helps! We are planning on doing the same thing to the Trex bed next to it as the tree roots are now showing up in it. I refuse to give up gardening, and I don't want to EVER have to dig out tree roots again. Mother Nature will always win!
Q
Cottage bdrm
Q