I Might Have Broken The Frost Bite Quest

So I started the Frost Bite quest a little while ago. I had previously done the quest as a Warrior and everything worked fine, and I'm currently doing it as my Archer. I got to the part where I needed to use a key to unlock Theorick's mansion door, but the key was refusing to work on the door. I tried both right-clicking and left-clicking the door with the key, but nothing was happening. I checked my quest book, but for some reason it was still telling me "Complete the puzzle and bring lava back to Eppo." (which I already did some time ago).

I had previously logged off of Wynncaft in the middle of Eppo's dialogue when I gave him the bucket of lava so I could deal with something in real life. When I rejoined, I had the stick that melts the ice, and I proceeded with the quest as usual. I suspect that me logging out during this part might have broken the quest (somehow).

After realizing this, I got rid of the key and tried retracing my steps so that I could fix the quest. But after I got the lava again, Eppo refused to accept it and instead did his dialogue again about us riding horses to Theorick's mansion.

At this point, I have no clue what to do as I have no way to get another key to the mansion since Eppo isn't trading my lava for the melting stick that lets me get the key. And I've already tried relogging and switching worlds. Any suggestions would be greatly appreciated!