Digging a bit more, I found that "pi" is an American spelling of "pie", and that OSPD4 doesn't list "pyeing", so the SOWPODS entry must be British. OED2 says, "To make (type) into 'pie'; to mix or jumble up indiscriminately". It also says, "To put (potatoes, etc.) in a pit or heap and cover them with straw and earth, for storing and protection from frost", which also has a sense of jumbling. Here's an example for the latter:
"The Swedes are pulled, topped, tailed and put into heaps (about eight heaps per acre), which are covered with a small quantity of straw and mould to preserve them from the frost, and to have them ready for use in any weather. This system of pyeing turnips is a very common one in Norfolk, and it is difficult to decide whether the majority of good opinions is in favour of it, or rather of the other method, which is, "placing" the turnips from several rows side by side, so as to leave at least nine-tenths of the land vacant."
"This word pyeing, as made use of in an old Rule of Court, signifies the selecting the Declarations from that confused Manner in which they were brought in, and reducing them into an alphabetical Order, for the more ready finding them, &c. It is a Term yet in Use among the Printers, but here it signifies the Reverse of this, for they call pyeing the casting away the Letters out of the Frame, or Box, confusedly together; and this they call making Pye.
--R. Boote, 1781, An Historical Treatise of an Action or Suit at Law, 2nd edition, p. 69
This is in SOWPODS but I can't seem to find it in any other reference. A few Google hits show it in use in some archaic (something about sorting documents in a legal setting) or very discipline-specific (some sort of chemical process?) contexts. Anyone have any better information on this "word"?