In an effort to go the extra mile, I have done further research and will here produce additional references that I should think will definitely satisfy anyone who sincerely wants to know the answer to the question. This comes from the Teachings of the Living Prophets Student Manual, available online, in the section on "Apostles Are Special Witnesses of Christ."
“Occasionally . . . I have been asked a question. Usually it comes as a curious, almost an idle, question about the qualifications to stand as a witness for Christ. The question they ask is, ‘Have you seen Him?’
“That is a question that I have never asked of another. I have not asked that question of my brethren in the Quorum, thinking that it would be so sacred and so personal that one would have to have some special inspiration, indeed, some authorization, even to ask it.... There are some things just too sacred to discuss...."
...The witness of Jesus Christ which is given to the Apostles is more powerful than that which can be obtained by sight:
“They [the Twelve Apostles] are special witnesses for Jesus Christ. It is their right to know the truth and to have an abiding witness. This is an exacting duty upon them, to know that Jesus Christ is in very deed the Only Begotten Son of God, the Redeemer of the world, and the Savior of all those who will confess their sins, repent, and keep his commandments. The question frequently arises: ‘Is it necessary for a member of the Council of the Twelve to see the Savior in order to be an apostle?’ It is their privilege to see him if occasion requires, but the Lord has taught that there is a stronger witness than seeing a personage, even of seeing the Son of God in a vision. Impressions on the soul that come from the Holy Ghost are far more significant than a vision. When Spirit speaks to spirit, the imprint upon the soul is far more difficult to erase. Every member of the Church should have impressions that Jesus is the Son of God indelibly pictured on his soul through the witness of the Holy Ghost.” (Joseph Fielding Smith, “The First Presidency and the Council of the Twelve,” Improvement Era, Nov. 1966, p. 979.)
Now, the above curriculum material quotes two LDS authorities, Packer and Smith, and affirms what they say. The above material makes it clear in at least three ways that LDS apostles are not required to have seen the risen Jesus. (1) It is considered generally inappropriate even for other apostles to ask someone if he has had this experience. This makes it clear that the existing apostles do not ask prospective apostles if they have seen the risen Jesus. If it is not asked, then it is not required. (2) Joseph Fielding Smith states that apostles may have the privilege of seeing the risen Jesus "if occasion requires." This is another way of saying that not all apostles see the risen Jesus; only some see him if the occasion requires. (3) The apostles are said to have "a stronger witness than seeing a personage," and that this kind of witness ("of the Holy Ghost") is one that every LDS Church member can and should receive. This statement would be unnecessary and misleading if LDS apostles were expected to have had the witness of seeing the personage of Jesus.
Another reference that further confirms what I am saying comes from President Harold B. Lee. He reported that when he was sustained as a member of the Twelve, he was told, "Now you understand that you are now to be a special witness of that great event, meaning the resurrection of the Lord." Lee went on to say that in response to this charge, he closeted himself in a room and read the Gospels and also read about Christ's appearance to the Nephites in the Book of Mormon. He said that as he read these things the people in those books became more real to him than ever before. Lee concluded that he had as sure a witness as the apostle Paul had because "a witness more perfect than sight is the witness which the Holy Ghost bears to one's soul so that he knows these things are true. I witness to you with all my soul that I know, as the Spirit has born witness to my soul, that the Savior lives" (quoted in Bruce E. Dana, The Apostleship [Springville, UT: Cedar Fort, 2006], 176-77; see pp. 177-79 for additional references). Similar statements from Lee are found in Teachings of Presidents of the Church: Harold B. Lee, chapter 5 (see here).
It troubles me that any Mormon would issue a CFR on this point when it would seem, from this documentation, that the position of the LDS Church on the subject is clear. It troubles me even more that not a single Mormon acknowledged that what I had said was correct. Other Mormons on this forum should have been quick to point out to Vance that LDS apostles indeed need not claim to have seen the risen Christ. They should have cited these references, or other references like them. Did you really need a non-Mormon to point these things out?