I wouldn't use distilled water - it would be lacking major and minor elements that your fish have become accustomed to and need for osmoregulation. The difference in water parameters is prolly what did your fish in -
pH, temperature,
GH, etc.
Also, distilled water is considered virtually "pure", meaning that there shouldn't be any impurities in it such as
chlorine and chloramines, so a dechlorinator wouldn't be necessary with distilled water.
The fish you listed (except the neons in my opinion) are considered fairly hardy fish and would probably be ok with dechlorinated tap water. And like theesigs stated, the brown diatoms are normal and might go away once the silicates are used up. Regular,
small water changes will do wonders.
What I would do is 10% water changes (with dechlorinated tap water) in the 5 gallon holding tank every 12 hours. You can get the 29 ready to go by replacing the distilled water with dechlorinated tap water in the meantime. Once the 5 gallon consists of all water from your tap you can add them back into the 29 gallon.
Hope your remaining fish make it.
Mike