Battle With Quack Grass -- Part 1

Quack grass invaded my mom-in-law's garden and I'm set out to redo the garden and eliminate the invader.  This is not easy because the Quack Grass rhizomes which  stay deep underneath the ground, under ornamental plants roots, concrete, tree roots, weed blocks etc. remain alive and find their way through cracks and gaps between the mentioned obstacles and sprout out.  I can pull the immerging sprouts showing through the ground but I know that there are more roots remaining under neath the earth.

I don't want to use herbicide so here is my plan:

1. Dig out plants that can be transferred to flower pots, (Day Lilies, Daffodils, tulips).
2. Dig the earth to expose the roots and let the heat of the sun kill them by dehydration.
3.  Make a raised narrow flower bed, ( no more that 20 inches wide) surrounding the existing flowering bush such as roses, butterfly bush etc.
4. IT IS VERY IMPORTANT NOT TO USE EDGING OR WEEDBLOCK AS THIS WILL ONLY BE USED BY THE QUACK GRASS ROOTS TO HIDE UNDER, instead dig a 4 to 6 inch deep trench around the flower bed.  
5. Monitor this trench and remove any Quack grass roots that is trying to cross over the garden area.  Quack Grass rhizomes seek damp soil to keep the roots alive and it cannot cross over a dry soil, so keep the trench dry.  Water only on the middle of the flower bed or directly over the plants.
6. Inspect individual plants often and remove new sprouts/rhizomes of  Quack Grass.  
7. Mulch minimally and apply it only at the bases of ornamental plants.  Keep the open areas in the flower bed dry and without mulch.  Inspect the base of the plant for the presence of Quack Grass often and remove rhizomes as soon as detected.

Day 3 of the Battle against Quack Grass:  I have dug most of the plants that can be potted, except another clump of Day Lilies.  I'm on number 2 on my plan.  Hopefully, I can finish digging up and re-potting the remaining Day Lilies today.