THis answer presents the view that the firstborns will replace the Cohanim at the Temple service sometime in the future.
While flipping through the Mishnayot (mainly Kodashim) I didn't see mentioning the practical Halochos for the time of that change.
I'm a true newbie in this subject, but I see a certain contradiction - the current Mishnayos target for the Third Temple (I presume, there's no need to learn Halochos that will not ever return), but they deal with Cohanim, not firstborns. Why?
Are there Halachic sources for the differences of the service of the firstborns לע"ל vs Cohanim?