Here in Mosiah 29:18, it appears that Hyrum Smith omitted the title king from before Noah when he copied the text from 𝓞 into 𝓟. Oliver Cowdery restored king when he proofed 𝓟 against 𝓞. The text allows for examples of both king Noah and Noah (that is, without any preceding king); elsewhere there are 23 instances of king Noah and 8 of Noah. The text uses Noah without a title the first three times he is mentioned in the text, once in Mosiah 7:9 and twice in Mosiah 11:1. The text then turns to using only king Noah up through Mosiah 19 (12 times). In Mosiah 20–21, there is some variation, with one occurrence of “the priests of king Noah” (in Mosiah 20:3) but two of “the priests of Noah” (both in Mosiah 21:23). Then we get nine straight occurrences of king Noah until the end of Mosiah 23. So when we arrive at Mosiah 29:18, we have not had a reference to king Noah since the end of chapter 23. One could argue that the sudden appearance of Noah alone here in Mosiah 29:18 bothered Oliver as he proofed 𝓟 against 𝓞 and that even though 𝓞 read without king, he decided on his own to add it.
The problem with this proposal is that there is no independent evidence that any of the scribes ever emended any instance of “king ” to simply the name or vice versa. In fact, here in Mosiah 29:18 is the only case where the text shows any variation with respect to whether king should precede the name of a king. As a related example, consider king Mosiah versus Mosiah. Initially, Mosiah is referred to as simply Mosiah (seven times), but once he becomes king (in Mosiah 6:4), he is subsequently referred to as king Mosiah in Mosiah 6–7 (four times). King Mosiah is not referred to again until Mosiah 22, and then we get considerable variation between Mosiah and king Mosiah. And for those instances in 𝓟 where Oliver Cowdery was the scribe, we find that he never once emended the text by adding king to Mosiah, nor did he ever remove an instance of king from before Mosiah:
Note especially that the Mosiah in Mosiah 22:14 is the first occurrence of Mosiah after a rather long interval during which king Mosiah has not been referred to, yet Oliver did not feel impelled to supply the title king. The probable reason is that 𝓞 itself did not read king Mosiah at that point. After scribe 2 of 𝓟 took over for Oliver Cowdery in Mosiah 25:14, not once did he emend any instance of Mosiah to king Mosiah (or vice versa), similarly for Hyrum Smith, who briefly substituted for scribe 2 at five different places in 𝓟. Thus it seems more likely that Oliver Cowdery’s correction of Noah to king Noah in Mosiah 29:18 was because 𝓞 read king Noah, not because Oliver felt that king was missing before Noah and needed to be supplied.
Summary: Follow in Mosiah 29:18 Oliver Cowdery’s correction in 𝓟 where he inserted the title king before Noah; Oliver was most likely correcting to 𝓞, which is not extant for this part of the text.