1.Goto Sender station. 
2.Make sure you have at least 2 Life Petals. (You can only get one at a time, but
  they respawn when you leave the area and re-enter. There's one in the Mystech 
  tunnels, and one to the right side of the entrance to Pump 7, behind a tree in 
  an alcove.) 
3.Goto one of those vender robots, and buy some Shamfoofa Shells. 
4.Then choose the "Sell your rare item" option, and there should be a "Twin-Scaled
  Underplate" option. Sell that. You get a good sum of money for each one you sell.
  Only the count of Shamfoofa shells is detracted, not the Life Petal count. 
5.Repeat: buy lots of Shamfoofa shells, and then sell the Underplates.

Note: that this also works for some other items that the vendor sells, but the 
Shamfoofa shells produce the best results.