The wood chips might improve the soil by next year. This year, though, many of the plants in the wood chips are really struggling for various reasons. One of the supposed selling points of wood chips--that they regulate water in the soil--does not seem to be true in our conditions. In some places, even though there's several inches of wood chips, and we've had a lot of rain, the plants seem to prefer as frequent watering as they did when the ground was bare and tilled.
The cardboard/straw combo was almost disastrous. The cardboard did kill the grass, but it also turned some areas of the garden into a swamp. We planted strawberries into the cardboard and straw. The berries started to develop root rot, and I subsequently stripped back the straw and cardboard and planted cover crops--which I should have done very early in the season. The plants did recover, finally, but it was a bit of a panic. The straw worked well in suppressing weeds and keeping the ground moist, but the depth needed adjustment through the season. Some of the strawberries are thriving and others are struggling.
It seems like every gardening method is sold as a panacea using religious language, e.g. "back to eden wood chip mulch", but any given method might not apply in every given soil situation and might not apply uniformly through the year. It will probably take several years of planting, adding compost and other amendments to really improve our situation and to learn what's going to work on our property.