Answer: I am not sure why you would have so much salt in your asparagus beds. Although asparagus is relatively salt tolerant and salt may sometimes be suggested for weed control for that reason, in modern practice it is generally recommended to mulch them rather than use salt as a weed control. But if you used a lot of salt, then it might cause problems. If you are watering your asparagus, make sure to water slowly to minimize runoff to surrounding areas. You maybe able to grade the area surrounding the beds very slightly to direct any runoff away from your other plants. In any case, leaching is the only way to remove excess salt. You could try a deep watering twice in succession to try to push the salt below the level of the grape roots, but there is also the risk you might drown your grapevine. If there has been ample rain since you applied the salt, the rain may do at least part of the job for you.
But, based on your description, I am not certain that salt is actually the problem. There is a fungal disease, for example, that causes cupping very much as you described. There is a photo of it at
And, another disease, phomopsis, can cause dark streaks along the vine
I would strongly suggest you consult with your local county extension to obtain a more specific diagnosis of the problem(s) and based on knowing that, determine how to proceed. If it is something that requires spraying for control, they will have the most up to date recommendations on what to use and how/when to use it. I'm sorry I can't be more definite for you long distance.
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