Hi,
You have got good mature plants and these are Phalanopsis, and read the wonderful sticky "Phal abuse ends here". Lots of information.
I too received the plants in similar situation, tightly packed in Moss. but I had few holes at bottom..
I think its better and its easy for you get some professional potting mix as you are from USA easily from ebay/amazon or any garden store.
If you can't opt for specialized pots, find some transparent plastic boxes and make plenty of holes to them (boxes should not be big, they should be just enough to accommodate roots of Phals)
Follow this link, I found it easy guide for re-poting
Untitled Document
As, said by Philip and others, Moss is highly damaging. And I guess the moss used is of very bad quality