First thing is to plot out the soil profile for the area. Remediation measures depend very much on what type of soil you have, whether clay, sand, silt or loam and what mixture of each. Clay will be very hard to work with, and remediation will be slow compared to sandy loam since the salt binds more closely to small particles. Sample the soil from many spots including those that appear to not have a problem.
If you find clay then consider improving the drainage in that area if possible by changing the soil profile, ie by building up the humus content or adding sand. Once irrigation water can flow quickly through the surface soil remediation will be quicker and more effective.
Also consider that there might have been an equipment malfunction at that spot, say a large spill of fertilizer which would result in high salt readings for that area.
Rain water and snow melt are reliably non-salty and with the passage of a few years could clear the problem if the soil is cooperative.