I have a lot of weed roots in my garden and nutsedge and I can literally shovel off a layer of roots easily. The garden is deep and drains well so that part is not the problem but it can be a problem getting through the root layer just to plant. Unfortunately most of my weeds are not killed by just topping them so the roots do grow back, I tried no till but I still needed to add compost to the soil since the compost sinks every year. My base is red clay. I don't really know how else to work more compost in without tilling.
I usually remove most of the plants and send it to the composting facility and I only tilled in the soft things like bolted lettuce, vegetable scraps, and eggshells from the kitchen waste. I am thinking of tilling in more of the stems from the garden instead of just the leaves. I am not worried about the extra nitrogen demand since I use sulfate of ammonia and apparently still have too much judging from the size of my kale and onions. I actually want to experiment on turning in a larger volume of garden waste as a scavenger. Usually I plant Asian greens for scavengers. Eventually, it should all break down and return the nutrients which should reduce my nitrogen requirements even more. I am only planning on using the smaller stems, the larger parts and roots still will go to recycling. I will have to machete or use two machete (Chinese food processor) the stems and it is too much work on the hardest stuff. It doesn't always work in the garden to leave roots behind. I pulled out some old Swiss Chard once and threw it to another part of the garden and it kept on growing.
I don't have space or enough browns for a compost pile and it attracts too much vermin so I primarily do worm composting. It still attracts a lot of roaches though, but takes up less space and the worms do the turning. I primarily feed them kitchen scraps and weeds from the garden. Stems and branches still go to the city recycling facility. In the tropics, most trees are not deciduous. The only deciduous trees in my yard are the plumeria and they have plumeria rust of the leaves need to be disposed of every year. BTW plumeria are native to Mexico, Caribbean, Central America down to Brazil. They are very common plants especially in the drier parts of Hawaii, but they are not native. The other trees and shrubs, drop only older leaves and I prune them to keep them in check. It would be the only time I would have enough for a pile but the pile would only have one source.
If I till in residues, do I mix it in to the soil evenly or do I do trench composting?
When I mixed corn stalks in the soil before, the one drawback was that it was hard to get a smooth top layer for planting with all the pieces of stems sticking out.
Should I keep some of the soil unmixed just for the top or just put a an inch or two of compost over the surface to make it smoothe and plant through that?
Mulching with the harder residues sounds like a viable option for some of the thicker stems. I usually use newspaper as mulch since it slows the weeds for a while so the veggies can get established but it doesn't block water from getting trough. I have fewer problems with it than with leaf or bark mulch where the weeds just grow on top of it and I have to water the mulch before the plant sees any water. I can use the stems in other parts of the yard not just in the veggie garden.
Happy gardening in Hawaii. Gardens are where people grow.