The original manuscript is not extant here. But the reading bodies seems more reasonable than the reading with the singular body. Verse 12 consistently uses the plural bodies and spirits:
Similarly, the beginning of verse 13 refers to the plural spirits (“the spirits of the righteous”) but then suddenly and inexplicably refers to “the body of the righteous”. The word righteous refers to a plurality; thus we expect “the bodies of the righteous” as well as “the spirits of the righteous”. The following clause does use the singular for both spirit and body, which suggests that “the body of the righteous” was an error introduced by this immediately following conjunct of singular nouns (“the spirit and the body”). The 1953 RLDS edition correctly emended the text here to read bodies. We also have the following example in support of this emendation:
Even though the verb phrase “are reunited” intervenes, the text here definitely refers to ‘the souls and the bodies of the righteous’, just like in the emended text for 2 Nephi 9:13.
Alison Coutts (personal communication) has brought up a question regarding the syntax of the third clause listed above (“and the spirit and the body is restored to itself again”). Here two singulars, spirit and body, are conjoined to form a plural subject, yet the verb is in the singular (is) and the following reflexive pronoun is also in the singular (itself). In this instance, we have what can be called a distributed plural, which basically means that ‘the spirit and the body is each restored to itself again’. In modern English we expect something like “the spirit and the body are restored to themselves again”, yet this clause in 2 Nephi 9:13 has never been edited in this manner at any time in the history of the text. Usage elsewhere in the text shows this same kind of distributed plurality with respect to spirit and body (as also with respect to limb and joint):
In both of clauses, the modal verb shall does not show number, but the use of the singular its maintains the individual distinctiveness of each conjunct in the subject. Nor has either of these uses of its ever been changed to their in the history of the text. The singular usage in 2 Nephi 9:13 (especially the is) may seem odd, yet it appears to be fully intended.
Another possible example of distributed plurality is found in the previous verse: “wherefore death and hell must deliver up its dead” (2 Nephi 9:12). For that example, the its was edited to their, unlike the examples listed here.
Summary: Follow the 1953 RLDS emendation in 2 Nephi 9:13 so that the plural bodies occurs with the plural spirits (“the paradise of God must deliver up the spirits of the righteous and the grave deliver up the bodies of the righteous”); the distributed usage in the following clause should also be maintained (“and the spirit and the body is restored to itself again”).