Tilling/Digging in a Forest Garden

I have a small forest garden in my backyard in Central Indiana. I have peaches, apples, pears and cherries planted (all dwarf or semi-dwarf due to space constraints) and they are all producing. I have a few shrubs (Goumi and Nanking Cherry) but would like to plant more perennial and annual vegetables starting next Spring. The problem is that I have wildflowers and herbs currently occupying the understory of these fruit trees. What are some methods to get rid of the wildflowers and herbs to plant other edible vegetables without digging/tilling and disturbing the soil? I can mow them down at the end of the season and mulch in place, but I'm afraid that they will just come back next year unless I dig or till to plant the new species I would like to grow. If anyone has any experience with this or guidance they can provide, I would appreciate it.

I have done this in a number of areas.  I just make a small hole where I want the new bush and plant right inside the existing plants.  I've never had any problems doing it that way.  I wouldn't worry about getting rid of any of the existing things, just plant in them.  If they get too tall and want to shade out small shrubs, surround the new shrub with cardboard for a foot or so all the way around.  Cover the cardboard with mulch if you like.

My forest garden has poor soil(filled with rubble from a foundation).
I just dig a little, then I go up,into a mound, raised bed , hugel thingy.
Blackberries seem to love this the most.

Thanks for the quick responses. I like the idea of sheet mulching around existing trees and bushes and just digging/planting the new plants where I want them. I'll give that a try this fall or early next Spring if possible and let you know how it goes.

Like Todd, I just plant what I want for any particular space and if the competition is to great, I use a sickle and cut down the offender. Once the new plant is established it will do just fine since usually these shade out the other stuff that was there first.
My only persistent offender is the wild blackberries, those I rip out by the roots as they try to make a comeback.

In a food forest shallow tubers that grow just below be the surface or under mulch are best. Sunchokes, groundnuts, hog peanut, and both potatoes and sweet potatoes can be grown and harvested without disturbing other roots.