Once a player reached level 60, they are offered a quest.. a difficult one, one that might take skill, luck, and brains to complete (not just the ability to read a how-to-rebirth-in-glitch website). Upon completion of that quest, the player is offered a new "permanent" skill that stays with them for the rest of their days, no matter how many times they rebirth. Then their skills and level are reset to level 1, and they get to begin again. They are... reborn! All of the skills are available to learn again, all of the quests are available again. In this setup, I do not think badges should be lost. But then there are new "rebirthing" badges that are able to be earned.
The rebirth skills would not necessarily be "advantageous" to have, more like cool or fun to have.. such as a "dance" skill that might allow them to give another player (or themselves) the moonwalk buff for a short time.