Hold To The Rod has an excellent answer. Additionally the Church of Jesus Christ of Latter-day Saints encourage its members to:

So we continually seek truth from all good books and other wholesome sources. “If there is anything virtuous, lovely, or of good report or praiseworthy, we seek after these things.”¹

This could also be exemplified when examining Dieter F Uchtdorf's talk Daily Restoration footnotes:

Jesus taught, “I am the way, the truth, and the life” (John 14:6). The NIV First-Century Study Bible contains this explanation: “The image of a path or way in the Hebrew Bible often stood for keeping the commandments or teachings of God [see Psalm 1:1; 16:11; 86:11]. This was a common ancient metaphor for active participation in a set of beliefs, teachings or practices. The Dead Sea Scrolls community called themselves followers of ‘the way,’ by which they meant they were followers of their own interpretation of the path that pleased God. Paul and the first Christians also called themselves ‘follower[s] of the Way’ [see Acts 24:14]” (in “What the Bible Says about the Way, the Truth, and the Life,” Bible Gateway, biblegateway.com/topics/the-way-the-truth-and-the-life).

So while the LDS church uses KJV primarily this is not the only version of the bible that can be used or studied.

Crucially, a stance that most missionaries would know about and reiterate?

No official stance on any other version of the Bible beyond KJV (see HoldToTheRod's answer). The missionaries of the LDS church do have stricter guidelines on what resources they can rely on:

• Scriptures (official KJV, Book of Mormon, Pearl of Great Price, and Doctrine and Covenants): Another note is that if the LDS church publishes scripture sets (quads) that are KJV and contain LDS footnotes
• General Conference addresses
• On Holy Ground
• Preach My Gospel
• Saints: The Story of the Church of Jesus Christ in the Latter Days²

So they can't reference other versions of the bible directly. (I've personally led discussions in the past or see in church where other's read from another version, and it doesn't usually have enough of a difference to mention)

On a practical level, would the NJKV be a safe choice to memorize and recall for discussions?

Probably not (see above about missionary library-if this is for LDS discussions...if this is for your own discussions go right ahead, keeping in mind if you want to discuss doctrine with the LDS they will usually reference KJV). Should be fine using it as a reference or for understanding/explaining in certain cases. No church restrictions on reading other versions of the Bible.

Or would it become just as futile as an NLT when there are word/phrasing differences?

This in part. Using the same reference material that the majority of LDS members/missionaries use be of more use IMO (again depends on use case exactly)

Sometimes, when I talk with LDS missionaries about passages in scripture, they'll reject some verses I have memorized because they are NLT or NIV

This is even the case for KJV, when you consider the JST (Joseph Smith Translation)

_{1 What is Truth, Seek Truth}

_{2 Your Missionary Library}

Hold To The Rod has an excellent answer. Additionally the Church of Jesus Christ of Latter-day Saints encourage its members to:

So we continually seek truth from all good books and other wholesome sources. “If there is anything virtuous, lovely, or of good report or praiseworthy, we seek after these things.”¹

This could also be exemplified when examining Dieter F Uchtdorf's talk Daily Restoration footnotes:

Jesus taught, “I am the way, the truth, and the life” (John 14:6). The NIV First-Century Study Bible contains this explanation: “The image of a path or way in the Hebrew Bible often stood for keeping the commandments or teachings of God [see Psalm 1:1; 16:11; 86:11]. This was a common ancient metaphor for active participation in a set of beliefs, teachings or practices. The Dead Sea Scrolls community called themselves followers of ‘the way,’ by which they meant they were followers of their own interpretation of the path that pleased God. Paul and the first Christians also called themselves ‘follower[s] of the Way’ [see Acts 24:14]” (in “What the Bible Says about the Way, the Truth, and the Life,” Bible Gateway, biblegateway.com/topics/the-way-the-truth-and-the-life).

So while the LDS church uses KJV primarily this is not the only version of the bible that can be used or studied.

Crucially, a stance that most missionaries would know about and reiterate?

No official stance on any other version of the Bible beyond KJV (see HoldToTheRod's answer). The missionaries of the LDS church do have stricter guidelines on what resources they can rely on:

• Scriptures (official KJV, Book of Mormon, Pearl of Great Price, and Doctrine and Covenants): Another note is that if the LDS church publishes scripture sets (quads) that are KJV and contain LDS footnotes
• General Conference addresses
• On Holy Ground
• Preach My Gospel
• Saints: The Story of the Church of Jesus Christ in the Latter Days²

So they can't reference other versions of the bible directly. (I've personally led discussions in the past or seen in church where other's read from another version, and it doesn't usually have enough of a difference to mention)

On a practical level, would the NJKV be a safe choice to memorize and recall for discussions?

Probably not (see above about missionary library-if this is for LDS discussions...if this is for your own discussions go right ahead, keeping in mind if you want to discuss doctrine with the LDS they will usually reference KJV). Should be fine using it as a reference or for understanding/explaining in certain cases. No church restrictions on reading other versions of the Bible.

Or would it become just as futile as an NLT when there are word/phrasing differences?

This in part. Using the same reference material that the majority of LDS members/missionaries use be of more use IMO (again depends on use case exactly)

Sometimes, when I talk with LDS missionaries about passages in scripture, they'll reject some verses I have memorized because they are NLT or NIV

This is even the case for KJV, when you consider the JST (Joseph Smith Translation)

_{1 What is Truth, Seek Truth}

_{2 Your Missionary Library}