You said, “As far as we know all resurrection bodies are alike.” Wasn’t Lazarus resurrected to a natural body? And what about the saints that were resurrected and seen in the Holy City when Jesus was resurrected, were they resurrected to a glorified body as the Church will be, and if so, where are they now, or where will they be in the millennium?
Lazarus and the others in the Bible who had died and been brought back to life were resuscitated in their current bodies, not resurrected into new ones. We know this because they all died again later. Resurrection bodies are immortal.
I believe the holy people who came out of the tombs at the time of the Lord’s resurrection were given new bodies and are now in heaven with Him, and in the millennium they will be in Israel with other resurrected Old Testament saints.
I also believe one of the capabilities of a resurrected body is to appear in natural human form as well as in glorified form. From His various post-resurrection appearances it’s clear the Lord did not walk around for 40 days after His resurrection in a glorified form like He was in Rev. 1:13-16.