I'm not sure, but if you have already received the quest then using the fix (which just replaces the relevant quest files with their fixed and cleaned up counterparts) might not have any effect.
However, the
notes for this quest in the Wiki here make no mention of buggy quest logic - just that it does not work in the original game because the quest file names do not match (and hence the quest does not appear in the game at all). Perhaps something else is causing the glitches you experience?
Have you tried for example spending more time in the town before fast travel? Going outside of the town and initiating fast travel from wilderness? Getting another quest from a guild? etc.