At some point he must have realized this, so effectively used some type of filler at the bottom of the cipher. Had the original message finished with "stop my collecting of slaves for the afterlife", rather than grammatically inferior "stop my collecting of slaves for my afterlife", the original message would have been the full 408 characters (shown above). It may be the case that once he realized his mistake of missing a line - and knew he now had only seven rows comprising the ciphertext to the Chronicle - he lost his train of thought. The accuracy of the remainder of the message regarding "THE" or "MY" was now an irrelevance.
The Zodiac Killer only used the word "LONE" in his address to the San Francisco Chronicle when requesting they print the cipher, so it's fitting that this word should have begun the ciphertext he mailed to them. The use of "STRAY PEOPLE" featured in the communication to the Vallejo Times-Herald, thereby completing the phrase "all the lone or stray people" that ran through rows 16, 17 and 18. The missing line (added in the diagram above left) only uses words from his July 31st 1969 letters.
Attempting to find an answer to the "18 unsolved characters" relies on the assumption that his original encryption was correct, which clearly it wasn't. The Zodiac Killer certainly misspelled words in his communications, but rarely, if ever, did he omit words entirely. If the Zodiac Killer had written his original plaintext grid of 17 by 24 into three separate and distinct sections, it's highly unlikely this mistake would ever have occurred (so it's likely he didn't). When reading text in any form, it's easy to accidentally skip a line or read a line twice. The former may have been the case with respect to the Zodiac Killer.
Thanks to Dave Oranchak for first floating the idea of a missing line, which I now believe is the likeliest answer.