As Eckler suggested in his article, vowels are one key to an efficient search for six-row solutions. To further expedite my search, I subsorted the candidate words by number of vowels and repeated letter. One can also use the symmetry of solutions to search only for words which alphabetically follow previously-found positions. My corpus of words includes some 237,000 words of lengths between five and fifteen letters. 302 solutions emerged, several of which were particularly interesting.
Longer mnemonics are most memorable if they form a phrase or sentence.
Each of thes above tricks involves two-card piles, or equivalently pairs of letters. We can first solve the trick where letters are repeated triply. The major complication will be that any given letter may have its three occurrences all in the same row, in two rows, or in three different rows. I was surprised to find only 19 solutions of this tableau in a large word list. You would lay down successive triplets of cards in positions corresponding to repetitions of a single letter.