Hi M
First, could you give us an indication of the soil type? Clay loam? Silt? Sand?
This bed is established and in its own way is already perfect. You only need it more manageable. A good solid hugel bed needs the interior wood to be sealed off completely from sun, wind and elements. That means no wood sticking up above the surface of the soil. It will continue to decay in the areas where the wood is not exposed, but the winds and the suns will prohibit humidity build up beneath the soil with encourages microbial activity. I never really understood the point of such tall hugel beds and have never made a tall one for this very reason. Just this spring I built my first half and half hugel bed. Most hugel beds I make are below ground, but this one was half under ground and half above ground. It was a pickle getting the soil to stay on even though it was only about 1-1/2 foot above ground and I have clay soil. I built it one month past and it still has the burlap on. it's the first time I've used burlap for soil erosion on a mound and I find it's working quite well. I had the kids help me pack the first two inches of soil. I watered well. I let it sit for three days to watch the soil's reaction. In our wind it quickly dried and cracked. Then, I added another 4 to 6 inches of soil atop and could see that there would be an erosion problem. I cut open some burlap bags and covered the mound in burlap.
Second, stop watering unless you live in a seriously arid climate. The established bed should have enough moisture beneath the top soil for the plant roots.
Third, if you choose not to break it down and make it shorter for manageability, you need more soil to add to the top. Hugel beds will, necessarily, have thicker layers of top soil depending upon the location of the wood beneath. There's nothing wrong with ten inches of soil in one place and only six inches in another area only one foot away. Plant roots are smart. They know where to go to benefit themselves. I find this amazing, actually. The humidity within a well built and sealed hugel bed is sufficient to sustain them for moisture except in the most arid climates if a plant is to thrive.
If you choose to break the hugel bed down, all you need to do is dig out enough wood to where it looks as though it's easier to manage. That part is a personal choice. After you backfill the soil (or add more soil) you can drape burlap cloth over the entire bed using heavy bricks to weigh it down or you can use some landscape pins to pin the burlap onto the mound. Of course, water this all very well. You're right about the weeds being the solution as the roots of the weeds will help keep the topsoil from eroding, but you can be picky if you want. It's your garden and you can manage it the way you need in order to enjoy the process or enjoy the results. It only requires a little more work and some patience to be selective about growies. After the burlap is on, slice some holes into the burlap to sow seed or place your transplants making certain the new sprout will have room to arise through the burlap easily. Eventually, the mound will establish itself. There's no way around weeding with perennial grasses and plants. They will try to grow through the burlap. You can manage this result however you see fit given the condition of the top soil. That's an environmental factor which only you can decide. You can mulch right atop the burlap, too.
I have heavy winds and the soil dries very easily even with the burlap. I cut holes in the burlap where I planted my pumpkin seeds. I place a brick right below the seeded spot on top of the burlap. The brick will keep the soil beneath it and also the seed soil moist so the seed can germinate without me watering it foolishly three times a day. And it did. I picked my most monstrous pumpkin plant to start on this. It's a plant I can depend on to grow under most circumstances to help establish that bed. I didn't waste my time with delicates, but then again this is a brand new bed and it will take some time to decay for more tender perennials and annuals. Probably by next spring.
Your bed is already established. You only need to spruce it up a bit and get it manageable. Just do what you must to get it more manageable and then plant, weed and enjoy.
bon