Here in the printer’s manuscript, Oliver Cowdery initially wrote “even unto the setting down in the place which I have prepared in the mansions of my father”. Oliver corrected setting to sitting by overwriting the e with an i. The level of ink flow for the correction is somewhat heavier, so it is difficult to tell here whether Oliver consciously edited setting to sitting or whether he was simply trying to copy the word accurately from 𝓞 into 𝓟. As explained under Helaman 14:4, Oliver normally copied the verbs sit and set without grammatical correction. Sometimes in the history of the text, the verb sit is found in transitive contexts; less frequently, the verb set is found in intransitive contexts. Virtually all these nonstandard uses were written without emendation in the manuscripts.
Here in Ether 12:37 we have the only potential example where Oliver Cowdery could have consciously emended the form of the verb for either sit or set. In contrast, the 1830 typesetter frequently emended the nonstandard instances of sit to set (see the examples listed under Helaman 14:4). The most reasonable assumption is that in Ether 12:37 Oliver corrected 𝓟 to sitting because it read that way in 𝓞. Oliver frequently mixed up e and i in his copywork, and that is what seems to have happened here when he copied the word from 𝓞 into 𝓟. He probably made the correction when he proofed 𝓟 against 𝓞, thus the somewhat heavier ink flow for the correction. (For another example of Oliver’s tendency to mix up e and i, see under 1 Nephi 22:4 where I discuss the competition between whether and whither.)
Summary: Maintain in Ether 12:37 the corrected reading in 𝓟, “even unto the sitting down in the place which I have prepared in the mansions of my Father”; in this case, Oliver Cowdery appears to have accidentally written setting, which he later corrected to sitting, probably when he proofed 𝓟 against 𝓞.