Our Hügelkultur adaption

We got our whole vegetable garden site excavated (9x9m), plus some space for fruit trees. Our yard looks awful now and the neighbours came over to ask if we are making a swimming pool. Unfortunately it looks a bit like this because of our miserable drainage.
The excavator sloped the whole area a bit, so at the bottom end we will lay some Agpipe with stones around and geotextile.
We will connect thes directly to the creek with something to shut the whole thing off in drought times. Maybe we connect the overflow to a pond as well.
The vegetable area will be caged with hardwood poles.

However I yet begun with the beds, to see a bit how they work out. I first made a30 cm layer of twigs and branches, which I cut in 15 cm lengths. Then I put a very thin layer of our "soil" , stones out. Then a layer of grass (from a lawn mowing company). Later there comes a layer of the earth the excavator dug out, but it is really very poor soil. Maybe I lay first a layer of grass sods.

I don't think that I really mounded form, we have enough sun here, but I must build up the paths in between the beds to the normal surface of the ground and that is 50 cm.
My first idea was to do this with bigger stones (the small ones would disappear in the beds) BUT 50 cm is pretty high and I reckon this gets too wobbly and the path will fall in my precious beds.
I don't want to use any kind of timber because of the costs involved. Is it an idea to pack somehow the stones with earth (we have enough of it)? Can this be done without boarding the paths up? And does this affect the thermal capacity of the stones ( I imagine they heat the beds up nicely, because we are on altitude).

Here's what I think you could have done with your excavation:  https://permies.com/permaculture-forums/5553_0/permaculture/bowl-terraces

Looks nice, but we must net our garden and I don't want it too big for that reason.
I begun one bed to find out how to proceed and I think I cannot simply fill in our soil for the paths because the drainage is bad. I know now that I cannot make the  path of stones alone, because the depth will be around 50 cm and my drywalls technique is not good enough . How about mixing big and middle sized stones with the soil for the paths, would the stones make the trick for the drainage? Would they warm may bed up even if it is mixed with soil?

I trialed a bit around and made the pathways with stones and the wet soil in between. That gets much more stable but it is not stable enough to build 50 cm up. I found some old roofing sheet offcuts in the shed and posts and this is what I will do:
I go to the tip for corrugated iron sheets. I will buy hardwood posts (they are cheaper than star posts)  and put the corrugated iron sheets around my beds. And then I'll backfill the soil. Maybe I put some smaller stones as a top layer to warm up.
This is the reason why Sepp Holzer only digs trenches, but in our case this would have created bathtubs. But I think with the corrugated iron around my beds there won't be too much water inside, however in drought the beds would rely on what comes from the top as the metal sheets would block moisture from getting in..

in 3 separate areas of my garden I did something kinda similar to what you are doing..

area 1..I piled about 2' deep wood chips and bark chips that were from our firewood, this was about 4x8 bed, covered with a mix of compost, clay and pond dredge soil..

planted it last year to potatoes and beans and corn and melons, everything did well except the melons.

area 2...I piled about 20 x 16 about 2' deep with wood scrap, mostly poplar, and compost from the compost pile that had been there, then covered with soil from the pond dig and some clay.

this area was planted to coles, tomatoes, potatoes, carrots, spinach, etc..

everything grew well except the carrots were small

area 3 ...I piled more compost mixed with wood bark, coveren the area with pond dredge soil mixed with compost, and planted this area with one dwarf frit tree, tomatos, mult onions, onions, chives and casbbages..also had some morning glories going up the tree.  everything in this patch grew very well..

these were allb uilt this spring and polanted shortly after building and msot of the plants did very well.

these were only a small part of our garden but they were most similar to what you are doing