Sandy loam is fine soil for propagating quack (often called couch) grass. In its place, quack grass is a fine herbage, but clearing it for a garden can be hard work since the roots form a thick mass which can be very resistant to a blunt spade. Sometimes you will hear a farmer say "Plow three times in August and it will be gone." However you have to be lucky and get a very dry August, otherwise the situation gets worse and not better. As a gardener would say, the advice is a load of old codswallop. (See the glossary for a discussion of this technical term.)
My preference is to tackle this job in two stages. In the first stage, assuming that the existing weeds have been mown to leave the stubble short, is to mark out the area to be dug and go over the ground with a sharp pointed spade turning over the soil in place. This does what plowing would do; it slices into the matted roots to break the soil into clods and turns the roots upwards to dry out and hopefully die in the strong sun. Continually turning the clods this way every few days would indeed dry out most of the roots. If you get rain interspersed, then the rootlets just keep on growing, and more vigorously and to a greater depth than before.
With the ground in rough clods, the second stage is to go through and remove the roots from the clods. It takes time, but done systematically the method works even in rainy conditions.
Here are some pictures of a reclamation effort in progress, taken on a warm November day.
In image 1 you see an overview of the area where a rectangle has been marked out and roughly dug, leaving the clods as rough as possible to dry. Careful inspection of the image shows the rounded shape of the clods which were dug with a round pointed spade. A square spade would be more appropriate in later years when there are no matted roots to be sliced apart. In this photo stage 2 is in progress, with about a quarter of the area processed for roots.
Image 1: showing clods in bottom left of garden area
In stage 2, I am working on each clod separately with a garden fork, breaking apart the clod and removing the roots. I am working from left to right, as far into the bed as I can reach with the fork without treading in the soil. Cleaned soil is piled to the left, and fresh clods drawn into the centre of the area for "processing".
Image 2: showing detail of root removal area
Adding the quack grass roots onto the compost in the fall does not seem to have any negative effect. The exposed roots dry out in the low humidity of winter and then compost down nicely in the spring after being turned a few times. Copyright © 2016
Image 3: showing barrow with roots loaded ready for compost heap