Digging up soil, how to proceed?

I am going to dig up some soil!

I have got a heavy clay soil, full of gavel. Pickaxes and mattocks just bounce off of it when it is dry. To make things worse, the soil is also full of huge rocks and concrete chunks, some as large as four feet across, right under the surface.

I have already tried sheet mulching. All this seemed to do was cut off my plants from any contact with the soil, which is good at holding water. We are blessed with a high water table, but this will not do my aboveground plants any good.

In some spots I dug deep holes and filled them with manure. In those areas, the plants are thriving.

A heavy duty standard rototiller did not work. It tilled down about two inches, with backbreaking labor.

I don't have time to plant years of cover crops. There are people putting time and money into this, and we need a return.

Even Eric Toensmeier wishes now that he had broken up the soil on "Paradise Lot" before sheet mulching.

Here are the rental options;

A mini- excavator or backhoe, which could scoop out trenches, but would be rather time-consuming.

A tractor driven rototiller, which could loosen the soil so that we could remove rocks by hand, but might get broken up by rubble.

A ripper on a light tractor, which might get bogged down by rubble, and which might not be maneuverable enough to get around obstacles.

Some sort of plow. The same considerations apply to this as to a ripper.

The eventual goal is to build "hugel waffle stone mulched olla watered beds" described in this thread: https://permies.com/t/37661/desert/hugel-sand-rocks-waffles-ollas But we can do the shaping and hugeling by hand if necessary, while there is not an expensive machine racking up hours. The main goal is to loosen up as much soil as we can in the four to eight hours that we have any machine.

Also, we need an excavating machine in any case to build some footings, and a massive gate arch. So something with a digging arm will be on site anyway. If necessary, we can rent a tiller, plow, or ripper, but that would be an additional expense.

I have found things with good taproots will rip through the soil when the rainy season is in place. Clover, Dandelion, Pokeweed, Dock.

High water table would probably be ideal for natives that grow there normally. Hazelnut, Chokeberry, Elderberry can all take seasonal wetness and drier as well.

Keeping a mulch on top should prevent a certain amount of drying, and prevent it from getting too solid.

http://www.garden.org/ediblelandscaping/?page=201101-how-to

I would not rent a mini excavator. It is far better having someone operating it, these guys are extremely fast and capable. Until you learn how to operate it you have spend more money in rent and fuel.
Otherwise I would sheet mulch. We have practically the same situation like you, but worse. After doing what you want to do in various forms, I do sheetmulch however
I do this only some months so far.
If you have something which can be called soil underneath the I would go for the excavator or other machinery but with the operator.

This what I use.

https://www.youtube.com/watch?v=QHEmnURcXdg

There are ripper teeth for excavators specially made to lift rocks, but you need a 10 ton excavator or bigger for those--at least to deal with the 4 footers.

I had a similar issue with clay, but only hit one rock--bedrock!--at 2 foot down.

My method was to use a subsoiler ON CONTOUR, fill those rips with woody material and manure/compost, then build raised bed on top of those riplines. I mixed compost and clay from the pathways to make the beds. They work like mini-swales. I only did 30" beds so I did one rip down the center. If you do 48" beds you may want to do two rips.

If you are going to use a tractor and subsoiler, use a small tractor--one that runs out of power or traction before breaking the subsoiler or 3 point. Also make sure your subsoiler has a shear bolt. Like this: http://www.northerntool.com/shop/tools/product_200439719_200439719 It isn't a good subsoiler for keylining (point is wrong) but is great for pulling up medium size rocks.

Similar to your waffle bed in idea but optimized to being built with the tractor and tools I had at my disposal.