Would first like to point out that although softened water does contain trace amounts of salt, it is not nearly enough to cause this disastrous level of corrosion in such a short period of time. Most consumers would probably weigh up having corroded pipes with soft water, or crusty pipes and hard water. If my pipes were going to rust like that, I wouldn't think of using a softener. Fortunately, this problem really only occurs with Lead pipes, or Coppper pipes that are already severely degraded when switched to softened water. If you have lead pipes and this is happening, I would recommend getting a plumber in to inspect the problem and visiting your Physician, who could help with Lead-poisoning issues.
Getting back on topic, I notice that you use H-E Washing Liquid. At least around here (on this forum), that stuff generally gets a bit of a bad rap when used frequently in machines due to the horrid residual substances it leaves behind - namely "snot" (Thick sludge, like outdated fabric softener) as well as staining in various parts of the machine. The cleaning ability of these liquids is also not good.
Since you use the washer on Hot, do you know if the machine is getting truly hot water when it runs, or is there a very long pipe run between it and the water heater than prevents the machine from getting good, hot water with the mediocre amount of water the washer probably uses? If there is a longer pipe run, then I would blame this issue on Cold (or Luke-Warm) water-washing combined with H-E Liquid not completely dissolving or being flushed away.
The best practice to avoiding this costly problem is to (at least monthly), ensure you run the tap nearest the washer until it is HOT, use POWDERED detergent and wash some old rags on the "HOT" setting, longest cycle with some washer-cleaner powder added for good measure, and perhaps Chlorine-Bleach. The better cleaning ability of the powder will ensure that the rubbish left behind from the liquid is flushed away, and adding the towels ensures the outer-drum of the washer is cleaned to some extent.