I'm no expert - But I'd say the plastic (I'm assuming you mean like a  
plastic carrot bag) is not letting enough air circulate. What we did  
this year is trim them pretty roughly and quickly in the field, run  
them quickly through the washer, put them into new grain-type sacks  
(Corman Bag) and then right into storage.  Our storage is 34-35, and  
our humidity is 98%.  They seem to be fine, no slime. When we pack  
them out we scrape the tops, and do any final trimming on the roots,  
then wash them again quickly.  Seems like a lot of damn work doesn't  
it.  Lee