Solution: Alternative Orthographonology
Answer: DEN, TOOTH

Written by Mike Sylvia

Each of the twenty-five answers phonetically contains the spoken name of an English letter; for example, “BOUQUET” sounds like it ends with “KAY”. With one exception, the answers can be paired such that replacing one answer’s spoken letter with another one produces the other.

1st word Letter from 1st word Letter from 2nd word 2nd word
INVEIGH A U IN VIEW
BEAZLEY B Y WISELY
CEASE C W DOUBLE-USE
RODDY D Q ROCK YOU
SUSHI E F SOUS CHEF
PIDGEY G P PIPPI
SAY CHEESE H R SARIS
FLY I M PHLEGM
JAMES J T TEAMS
BOUQUET K Z BOOZY
ELSA L V VISA
ARROW O S HEIRESS

This covers nearly the entire alphabet. By process of elimination, X (from the leftover unpaired answer DECKS) must pair with N, which implies one answer is the missing word DEN.

The pairs can form a bidirectional cipher key that can be used to translate the given string to “A WORD OF LENGTH FIVE AFTER EM OR BEFORE CUE ZEE”. “EM” and “CUE ZEE” in this context need to be translated once more with the key, giving EYE and DECAY, and thus the other answer is TOOTH.

Author’s Notes

“FISHY” in the ciphertext is, believe it or not, entirely coincidental, but the idea of FISHY being an literal red herring is amusing enough that I couldn't bring myself to remove it.