It will probably not help, since the quest will still want you to loot a specific fornsworn briar heart... ie it will point you to a dead, empty body. But normally it would be a good advice..
I got the idea from a combination of places I researched.
1. http://www.reddit.com/r/skyrim/comments/mfgrp/psa_you_can_transfer_skyrim_savegame_files_from/
and
2. http://www.uesp.net/wiki/Skyrim:Repairing_the_Phial
The first link explains how to transfer game saves from pc to 360 (or 360 to pc) as well as format conversions etc.
The second link claims this:
"Bugs
(360,PS3,PC) When you pick up the Briarheart, the quest will not update, and no option to turn them in will appear when talking to Quintus. Unknown cause (some author had 6 already but i was removed it with console it still won't work though). they cannot be dropped as they are now quest items. The way to remove any briar hearts from your inventory is to open console and remove the briar heart with player.removeitem 3ad61 1 code. The solution to complete quest is setstage MS12b 60 code. Make sure you do not have any Briarheart in your inventory when you take this quest."
All in all, I would try this myself but don't have the money to purchase another copy.
EDIT:
I'm thinking you could remove the heart from your inventory using a command. After you could wait a while for the forsworn to respawn (the briarheart with the quest item, etc.).