There is indeed a showdown after each event. Post-jam, that's going to be represented better through a sort-of procedural narrative.
The game is not supposed to stop at level two. If the issue is that you're stuck on the character screen after choosing where to place your new stat point, press ctrl to close it and you'll move forward.
Cheers for our old west RPG ambitions, by the way; it seems we shared some collective consciousness towards current and future plans for our games.