Here Joseph Smith edited the original preposition of to with, thus making the two conjuncts begin with the same preposition (“afflicted with all manner of diseases and with devils and unclean spirits”). Elsewhere, the past participle afflicted, when complemented by a prepositional phrase, is usually followed by the preposition with:
The example from Mosiah 17:16 uses the same phraseology as Joseph Smith’s editing of 1 Nephi 11:31 (“afflicted with all manner of diseases”). It should, however, be noted that for each of these four examples, the preposition could have also been by. In fact, in the example from 1 Nephi 16:21, the preposition by is the expected one in modern English since a human agent is involved (that is, we expect “having been afflicted by my brethren because of the loss of my bow”). There is one example with the preposition by, and here a human agent is also involved:
In archaic English, the preposition of is used as the agentive preposition (instead of the modern English by). For instance, in As You Like It, Shakespeare has “I have been told so of many” (meaning, of course, “I have been told so by many”). Consider, for instance, the following example in the Book of Mormon where the archaic of was accidentally replaced with by in the 1841 British edition:
One can therefore argue that the original use of the preposition of in 1 Nephi 11:31 is intended to be equivalent to the preposition by (that is, “afflicted by all manner of diseases”). Like the archaic usage originally in Mormon 8:1, there is no need from a textual point of view to emend the original of in 1 Nephi 11:31 to either by or with.
Summary: Based on the earliest textual sources, restore the original preposition of in 1 Nephi 11:31, where it serves as the archaic agentive preposition (in place of by, the modern one).