First, I would remark that the question "what happened to Jesus' body?" is not an easy one either for those who believe in a corporeal, physical resurrection... where is Jesus' body now? On a cloud, on another planet? What is the meaning of a physical body in a spiritual realm?
The NT texts which insist on a corporeal resurrection (e.g. Luke) are not the only ones nor even the first. They seem to react to a previous view implying a spiritual resurrection, or raising up, of Jesus.
In the Pauline texts Jesus is raised in spirit, or rather as spirit:
Thus it is written, "The first man, Adam, became a living being"; the last Adam became a life-giving spirit. (1 Corinthians 15:45)
In Pauline theology the body of Christ is given in the Eucharist (1 Corinthians 10:16; 11:23ff) and subsequently identified to the Church (1 Corinthians 12:22-27). Christ lives as spirit within Christians individually (Galatians 2:20; Philippians 1:23) and collectively (cf. Ephesians 1:22f). There is no allusion there to an "empty tomb".
The highly contradictory accounts of apparitions in the Gospels and Acts, progressively developing from Mark's Gospel where no apparition occurs, bear the distinct mark of pious legend. And the reference to eyewitnesses in 1 Corinthians 15 was probably added at a time when none of the supposed eyewitnesses could be questioned.
Add to that some vestiges of alternative endings in which, instead of resurrecting, Jesus doesn't die at all (e.g. the "young man" escaping when Jesus is arrested in Mark 14, then appears again in the empty tomb; the substitution story of Jesus Barabbas vs. Jesus the Nazorean; the cry on the cross in Mark and Matthew implying that the "Christ" who came into Jesus at baptism left him before death)... a corporeal resurrection was just one version among many before it became the official version.