It appears there was some amount of interference between the Hot Towel SPA project type and my project. I didn't start from scratch with Hot Towel, but added it to an existing project, so I believe there were some routing issues.
I deleted the HotTowel specific Configs (e.g. HotTowelRouteConfig) because everything that was done there I was already doing in my ASAX file.
After that everything worked fine.