How to apply to do a masters thesis in the US or Canada when departments don't post specific positions?

Master's have a different meaning in North-America than in Germany. While the Master's thesis typically closes the university studies in Germany, it is considered 'graduate studies' in North America (the Bachelor is considered the 'university degree' and the majority of students join the workforce with it). Masters are either specializations or given to graduate students who wish or have to stop graduate school before completing a PhD. That is the reason why you didn't find any offers for 'Master's theses' on institution websites there.

You approach of asking a local faculty for contacts is probably your best shot, don't give up. Narrow down to a few options and write them an email, explaining your skills, interests and field of study. Ask if they can think of a possible project for you. In your inquiries explain the requirements for a foreign Master thesis host at your university. Stress out the fact that you are merely asking for the right to use the local facilities and a co-supervision of your work. In my case, a professor told me about a project he had in mind, and I expanded it in a short proposal that was accepted by the local faculty and my program.

North-American professors have to worry about funding for their local Master students. You have to make clear that you want to be a visiting student and thus you will most likely be able to waive tuition fees (with some exceptions, like MIT). Along that line, explain that like Masters students in Germany, you will pay for your ramen noodles yourself and don't necessarily need a stipend if it can't be provided (on that note, Canada and the USA require that you prove you have sufficient means to support yourself while on their territory, so start a piggy bank).

With this in mind, there are few reasons for a group leader abroad not to consider your project, since you might contribute to their research while not costing anything. These few reasons include: too much supervision burden already.