Have to get rid of some elms... can I grow mushrooms?

So here's my situation. We bought a new house with a big yard, and the last folks were clearly not gardener types. There are a few flower beds from days of yore (with peonies, phlox, iris etc. in the understory) that have become volunteer forests consisting mainly of elm (American and Field) and Mulberries (White, I think.) I want to leave the mulberries to see how the fruit is, and possibly grow a bed of coppiced mulberry shrubs if its good. The elm isn't doing me much good, though, and is in fact shading the area that is best in the yard for our annual veg. garden. I'd like to take them out and replace them with polyculture heavy on the raspberries.
It will for sure be a challenge to get these guys out. The trees range from tiny saplings to 6 inches or so diameter, and probably at least 15 feet tall. We can try to pull them out by the roots with a car or something, but there's a fence in the way that will make all of that complicated. What I don't want is to accidentally copice these weed trees and have to deal with them all over again later.
So I'm wondering... if I cut them instead of pulling them, can I grow some mushrooms here, and maybe establish my raspberry bed at the same time?
Some facts for you:
-Once the trees are cut this will be a part-sun area (a big block of mid-day sun)
-It's not particularly close to water now, but we're working on fixing that (see also: annual veg garden)
-If this works well, maybe we'll try it with some of the 1 million lilacs growing along our fence line as well.
-I'm brand new to mushrooms.
So what do you think? Will mushrooms effectively keep them from growing back? Any recommendations of species or methods that could work in this situation? I know that Morels like dying elms... but is that too ambitious?

Field and Forest has a chart comparing different wood species to different mushroom varieties. Unfortunately the one on their website seems to be broken, or I would link you to it. According to the physical catalog of theirs I have, nameko and oyster mushrooms will both grow on elm wood. They don't sell morel spawn, so it's not mentioned by them. They also say the best time to cut a tree for mushroom growing is winter, when it's dormant. Hope this helps!

Howdy,
"you can indeed use plug spawn to hasten the decomposition of the stumps by growing mushrooms on them."

You can girdle the tree at or near ground level. Tree should die above the girdle, but may try to resprout/grow below, especially from roots. Digging around the stump and severing any roots you come in contact with, will aid in killing the main tree. You could then spore the trunk.

Girdling is cutting into the cambium layer, around the trunk. Multiple cuts, one above the other, 2-3" apart, make girdles more effective.

Ooh, this is useful stuff.
A few more questions:
1) What tools have you found most useful for cutting roots? Sounds like a big chore, best to have the right tools.
2) Favorite methods or resources for learning to do the actual inoculation part well?
3) Thoughts on growing other stuff in this bed at the same time? I'm thinking raspberries. Maybe I can do double duty - digging roots and installing a rhizome barrier at the same time?

Howdy,
Mattock is a below ground digging tool(heavy), one edge will chop roots, Pick is easy way to loosen soil, Pulaski is firefighting tool, axe head above ground cutting and root cutting hoe(also used to expose roots and cut with axe head), Trenching shovel, straight edge cuts roots, Tree plant, also helps cut roots.

I find the mattock to be a useful tool and maybe you could find a used one. It takes the same handle as a pick. Digging a trench around the trunk, narrow 4"wide or so, gives you room to work. You could be 3-4ft from the trunk if you wanted. You would be able to plant berries in the trench. I cannot kill blackberries and have to herd them around my place. I would keep my eyes open for tree sprouts between the trench and the tree trunk. A sawzall with metal/wood blade can also be used to cut roots and also to girdle, although because of the narrow blade, I would make more than one cut, 3-5, one above the other, 1 inch or so apart.

https://www.powells.com/book/mycelium-running-how-mushrooms-can-help-save-the-world-9781580085793  Find this book used

https://www.powells.com/book/farming-the-woods-9781603585071,  this book also, used

https://fungi.com/

You can now buy chainsaw bar oil that has mushroom spore in it. It may also be a non petroleum natural oil.

Hypsizygus ulmarius is one of the easiest and best tasting mushrooms to grow. It refers to elms in its species name.  I dare you  to inoculate the recently chopped trees with this mushroom spawn.
JohN S
PDX OR

Oh, perfect! Do you have personal experience with the Hypsizygus ulmarius? Any words of wisdom for a newbie?

I have grown them. They are one of the easiest ones to grow.  They taste great!  THe only advice I have is if you grow them in a bucket, use some ag lime to keep the ph up, because there is a green mold that can get to them.  If you grow them on logs, it may be easier to avoid the green mold.

John S
PDX OR