Other considered possibilities

• Oxcart - Does the 340 cipher's plaintext follow an "ox cart" path; that is, does it read alternately from left to right, then right to left?
• Vigenere
  • Vigenere encipherment prior to homophonic substitution
• Playfair
  • Playfair encipherment prior to homophonic substitution
• Bifid
  • Bifid encipherment prior to homophonic substitution
• Did the killer encipher the message, then re-arrange its lines?
• Many-to-many (one cipher symbol maps to multiple plaintext letters)
• Multiple encryption stages (examples: homophonic that has been rehomophoned, homophonic that has been transposed)
• Phonetic / nomenclator
• Was the cipher intended for use by its author only?
• Jarlve's tests
  • At the above link, Jarlve has documented the following variations: Cardan grille variant, stacked directional transformations, spirals, double spirals, column flips, double directional transformations, rail fence, row flips, and row flips in a 20 by 17 grid.
• Heiko's transposition ideas (more info)
• Word search
  • No decryption; simply look at the symbols as is, interpret them as plaintext, and read them out following different routes and directions.