Planting apple trees in a restrictive soil

I am planting a row of semi-dwarf fruit trees. There is about a foot of decent soil, but beyond that there is a very heavy clay subsoil with very slow water infiltration. The trees are semi-dwarf, so they tend to have smaller roots anyway. The land is sloped, so there won't be standing water. The climate is semi-arid. Given all those factors, I think I should be able to make this work? My biggest concern is a restricted rooting depth leading to water stress in the summer, but irrigation will be necessary for these no matter what.

Any thoughts or suggestions? I'd rather not plant on berms or mounds, due to site, time, and money constraints, and because it would make establishment watering more difficult.

Gilbert,

Do you know what is the thickness of the clay layer? if it's reasonably thin, for example 20" then it would make sense to dig the hole deep enough to remove the clay and replace it with clay/compost mix. When I encounter spots of clay, I dig it down as much as I can and make clay + coarse sand + compost mix. Also, some rootstock will handle heavy soil better than the other.

The restrictive layer is at least three feet thick, probably thicker. I don't want to amend the planting hole; Edible Forest Gardens and other resources suggest that his will paradoxically lead to pooling of water in the hole.

There are different approaches to tree planting. At the beginning I was planting "naturally" and everything was dying, also "naturally" in bad soil, with manual watering, no amendments and gophers. Later I have noticed that the spots that got deep ripped and disturbed produced extremely thick vegetation.
It's possible that mature tree will handle bad soil, but before it grows - it will be tormented (in my case) by extreme heat, late frosts, sun, winds, hard-as-brick clay (in some spots), gophers. Since I was losing a lot - due to simplified planting and vast array of species and cultivars I started improving things.

My current approach is:
-plant more moisture demanding trees at the bottom of the slope: all prunus, pears, quinces, chestnuts, higher I plant apples, pistachios, mulberries, persimmons and at the top olives, some figs, Italian pines, pomegranates
-avoid cultivars that were developed in oceanic climate of central Europe/Pacific North/humid Asia or from east of the Rockies
-if I encounter heavy clay I'm trying to put there prunus on Myrobalam rootstock
-I plant in January and February
-all plants (except older, large transplants) go into wire cage (1/2" openings), fi 12", height 16-24" to protect from gophers
-I dig a hole at least twice the cage diameter at 1.5 times the height
-the soil from the hole is mixed 1:1 with compost (eucalyptus chips + sheep manure)
-if the soil is heavy clay I use 1:1:1 soil, compost, coarse sand
-I mulch with wood chips
-if the tree is very thin or sensitive I put a protective sleeve
-they are drip irrigated with 2 emitters (40 l/h each) and irrigated for half an hour at a time (two irrigations in summer per week, 3 if temperatures are over 40 C)

After I tested multiple cultivars and implemented all improvements the trees are dying at much lower rate and they finally produce fruits - more every year.

Yeah a foot of decent soil over heavy clay is tricky but not a dealbreaker, especially on a slope. The fact that water won't pool is a big plus. I'd be more worried about the roots hitting that clay wall in summer and not being able to chase moisture down. Have you thought about mounding up a bit on top rather than trying to go deeper? Even 6 inches of extra soil on top gives the roots somewhere to spread laterally without fighting the clay.

Thanks for the suggestions! I'm avoiding amending the planting hole, not because I'm trying to do things naturally, but because I've read that it is a bad idea; I'm going to put the amendments on top of the soil. These plantings are going to be irrigated, fertilized, etc; I am not just planting them and hoping for the best.

Here is a link on the problems with amending planting holes, particularly in heavy soils; short term growth is improved, but long term it can create problems for the tree:  https://wpcdn.web.wsu.edu/wp-puyallup/uploads/sites/403/2015/03/soil-amendments.pdf

I read it and it makes sense, but I also believe that the small/young trees must be helped, because when I was not helping them they were dying and losing 30 trees per year (the worst when they die 2 years after planting)became exhausting. Of course 300 trees that I planted are not sufficient pool of data, because all of them were different species or cultivars and I can not in any scientifical way isolate what stopped their early demise. My strongest experience is what I mentioned before - disturbed/ripped soil (by buldozer) created conditions for lush growth. It's a very interesting topic. It's similar to dry farming - I read so many articles and some books before having my own orchard, but did not have enough experience to realize that what works for someone even few miles away will not work for me in my valley microclimate. Usually people talk about successful/existing orchards and do not focus on the crucial aspect of establishing pencil thin trees with no water.
Even after removing climatic conditions my case is different than yours just because my clay layer is maybe 20" thick (only in the western part of the orchard) and then decomposed granite starts to appear, so roots of my trees will need less time to drill into this lower layer with good drainage and better availability of nutrients. Also the fact that I stopped experimenting with traditional central European cultivars helped a lot.
One of my findings is that yellow European plums are weaker than purple ones and similar discovery for Apples - from 20 cultivars (all on Antonovka) I had, the following survived:
-Belle De Boskoop (blooming now)
-Black Oxford (buds opening)
-Spitzneburg (blooming now)
-Redfield (blooming now)
-Antonovka (yellow, but strong) with a lot of bloom and hopefully will produce something this year
-Bramley (blooming now)
-2 Dolgo seedlings (one blooming)

Russets were dying quickly and without exceptions.
I also have Lodi but its growth is arrested and after 5 years it's still 20" tall.
Grafting was always a failure.