Here in the printer’s manuscript, while editing for the 1837 edition, Joseph Smith inserted a not but neglected to change the following no to any; thus in 𝓟 he ended up creating a multiple negative (which is definitely not characteristic of his editing for the 1837 edition). Joseph probably changed his mind here and decided not to make any change but then neglected to cross out the inserted not. In any event, this change was not implemented in the 1837 edition.
The use of not directly after the verb seek is fairly common in the text (with seven occurrences), as in Jacob 4:10: “seek not to counsel the Lord”. But equally significant is the use of the adverbial phrase “no more” with the verb seek (with four occurrences besides the one in Mosiah 27:16):
The first two of these occurrences (in Alma 36) give Alma’s account of his conversion; here in Mosiah 27, Mormon gives his abridged version of the same event. We note the basic difference in the placement of the adverbial phrase “no more”: in Mosiah 27:16 it comes at the end of the clause, but in Alma 36:9, 11 it comes both times right after the verb. Thus the ultimate decision to reject the addition of the word not in the 1837 edition is appropriate since the original text for Mosiah 27:16 has the adverbial phrase “no more” and the original phraseology is very similar to the phraseology in Alma 36:9, 11.
Summary: Ignore Joseph Smith’s initial decision to insert a not after the verb seek in Mosiah 27:16; the original “seek to destroy the church no more” should be retained, especially since the adverbial phrase “no more” occurs in Alma’s own account of his conversion in Alma 36:9, 11.