Santa Fe had a siberian elm eradication program they were spending millions on every year. They some grad student doing his thesis pointed out 80% of the tree canopy in SAF is Siberian elm and it is already to hot to plant cottonwoods.
The news thinking in arid regions is to keep the Siberian elms as they will survive the coming heat and reduced rains.
In my area the only deciduous trees growing wild are Siberian elms and desert willow.
I would try planting understory shrubs , serve berries can make it under elms, maybe wild plum, jujube on the edges of the shade.
The States extension service will have some 411 as will Plants of the South West.
This years low cost Tree and shrub sale by the forest service is in July you get the starts in the fall. It's about $80 for 40 plants.
Most are for wind break and reclamation .
Make sure you test your soil for PH and know the type of soil ( sandy, clay etc.) work backwards from there. Parts of my property are
8.5 ph few things can deal with that. if your ph is really high like this consider inputting humic acid with micro rhizomes and
see if your community has chipped wood for low cost. I have spent a couple years working on my soil in small areas as I can.
Yellow clover can live with our paltry rain and get some of those mircrorhiza to get going and get some nitrogen in the soil.