One wonders here if the singular doing of the earliest textual sources isn’t an error for doings. The 1892 RLDS edition has the plural doings, perhaps unintentionally (yet out of expectation of the plural). The 1908 RLDS edition restored the singular. Elsewhere in the text, there are 21 instances of the plural noun doings but none of the singular noun (excluding cases where doing acts verbally):
These examples argue that the singular doing, the earliest reading in Mormon 8:35, is an error. If so, the final s must have been dropped in 𝓞 as Oliver Cowdery, the presumed scribe here, took down Joseph Smith’s dictation. There is considerable evidence that Oliver occasionally omitted the plural s, as in these examples that involve the ending -ing:
On the other hand, the singular noun doing is not particularly offensive here in Mormon 8:35. It has been maintained in both the LDS and RLDS texts. Moreover, there are similar examples of the singular noun doing in the King James Bible, although they all refer to the Lord’s doing:
(There are also a number of examples in the King James Bible of well doing and evil doing, which are somewhat different.) On the other hand, references to “one’s doings” is quite common in the King James text (there are 51 instances, some of which refer to the Lord’s doings). Since the singular is possible, the critical text will maintain the earliest reading here in Mormon 8:35, “I know your doing”, despite its uniqueness in the Book of Mormon text. The possibility remains that doing is a primitive error for doings.
Summary: Maintain in Mormon 8:35 the singular doing in “I know your doing”, the reading of the earliest text; there is some possibility that the original text read “I know your doings”; although there is no independent support in the Book of Mormon text for the singular, the King James Bible has examples of this usage.