Some if not all of Murder being a Crime that is a big one that is highly punished is because it takes away peoples work, the stats they built up. What if part of the scent time, or some of the severity the punishment might be reduced by electing to bury your victim properly? It would still be bad, and maybe even get you killed, possibly, but I was thinking some form of incentive towards burial for people other than the victim ought to exist, and maybe even for the murderer.
Also in general, provide some incentive towards burying all the dead bodies in town. Maybe a faith and wisdom, or a small silver reward for helping the Priest by bringing him a body, or what have you. If that's not appropriate, make them actually decay after a certain time to simulate the NPC's giving the player a reasonable period for their heir to collect any goods, and have it just finally decay/disappear. The first has player involvement. As it is you get nothing for expending materials on burial for someone else.
But I also like the idea of a murderer or criminal paying his dues/restitution that can potentially make things easier for them.