The original syntax here, despite its unusualness, is definitely intended since it is supported by a similar instance of this syntax later in this chapter:
By lining these two passages up, we can see their original parallelism:
| 3 Nephi 11:10 | 3 Nephi 11:15 |
| I am Jesus Christ | it was he |
| of which | of whom |
| the prophets testified | it was written by the prophets |
| that should come | that should come |
In the printer’s manuscript, Joseph Smith edited the first example (in verse 10) to “of whom the prophets testified should come” (changing the which to whom and omitting the that). The 1837 edition ended up with a different modal verb, shall, in place of the original should. This change may have been intentional (although the 1908 RLDS edition, following 𝓟 explicitly, later restored the should ). In the 1852 LDS edition, the preposition of before whom was dropped (perhaps intentionally) from the LDS text.
On the other hand, the second example (in verse 15) has basically been left unchanged. The that was dropped in the 1837 edition (perhaps unintentionally), but nothing else has been changed in this later example. In fact, the 1849 LDS edition restored the that to the LDS text. So in the current LDS text, the second example (in verse 15) remains unchanged from its original reading while the first example (in verse 10) maintains its fully edited form.
Basically, the first relative clause in both these examples can be treated parenthetically and set off by punctuation:
This means that the that in both verses is the relative pronoun that, not the subordinate conjunction that. This relationship is further supported by usage in the New Testament of the King James Bible. In each of the following similar expressions, the English he that and that reflect the Greek pronoun ho, not the subordinate conjunction hoti:
(Also note the use of should in both these King James examples, just like the two examples in 3 Nephi 11.) In other words, the that in 3 Nephi 11:10 and 3 Nephi 11:15 should not be interpreted as forming the complement of the verbs testify and write (which in each case occur in the immediately preceding relative clause). Instead, the relative pronoun that refers back to Jesus Christ (in verse 10) or to its pronominal equivalent, he (in verse 15).
Summary: Restore in 3 Nephi 11:10 the original syntax: “behold I am Jesus Christ—of which the prophets testified—that should come”; maintain in 3 Nephi 11:15 the parallel syntax: “it was he—of whom it was written by the prophets—that should come”; in each case, punctuation can be supplied so that the relative clause referring to the prophets can be kept separate from the main statement that refers to Christ’s coming.