I recommend Country Save Non-Chlorine Bleach on solveeczema.org as a laundry booster. (Not their detergent, obviously, just the non-chlorine bleach. Unfortunately, last I checked, the packages look nearly identical.)
In my experience, Country Save Non-Chlorine Bleach is probably the most helpful laundry booster to aid in superwashing.
I just did a load of hand-me-down kids’ clothing from a friend who uses detergent. I have sometimes had to wash the clothing (initially) a dozen or more times to get the old detergents out so my son doesn’t react. I have found that soaking the clothing with soap flakes and Country Save Non-Chlorine Bleach works noticeably better than soap alone or soaking with just water or soap. I still have to wash several times, but it cuts the number of necessary washes down considerably. So I will wash & soak with Country Save and soap flakes once or twice (or more, depending), then wash with soap, then wash with just water.
Borax works well as a laundry booster, too. It does a better job of removing old perfumes and scents than anything else I have tried. Please refer to comments and cautions about both Borax and Country Save Non-Chlorine Bleach in regard to superwashing on www.solveeczema.org .