The 1906 LDS edition replaced the modal could with should, undoubtedly because there are three should ’s in the preceding text. The 1906 edition never served as a copytext for subsequent LDS editions, so the secondary should was not transmitted into any other edition. In addition, the modal could is perfectly appropriate here in the resultive that-clause that follows the listing of those conditional statements (the conditional should is appropriate there). Both 𝓟 and the 1830 edition read could here in the last instance, which undoubtedly means that 𝓞 also read this way.
Summary: Maintain the modal could in the resultive that-clause in 3 Nephi 4:16.