Meta: Where's the "free for non-commercial use" license? I'm curious about the text.
If I did want to release a project as open source (not free software) under "free for non-commercial use" terms, what would be a recommended license? AFAIK none of the common open source licenses target this.
I'm not sure which distinction exactly you're drawing between free software and open source, but most open-source licenses don't aim to restrict how people use the software, for many reasons.
One reason is that it's just harsh. "Free for non-commercial use" means that if someone builds on your software to make something successful, they can only succeed on your terms. Sure, that may be what you want, but it's not what users want if they're going to take the time to understand your code.
While such code may technically be open source, much like the "shared source" initiatives of large software companies, the code won't be able to participate in the larger open-source ecosystem. Would you expect someone else to contribute to the code? Why would they? They'd be enriching your IP but they wouldn't get any additional rights to the code, nor would they get revenues from commercial licenses. Unless you hire them as an employee.
Also, restrictions on how you use the software violate the Debian Free Software Guidelines. Indeed you indicated that you're not interested in "free software", but you shouldn't expect to find "common open source licenses" that violate the DFSG.
Restrictions on use tend to be more tolerated in creative works than they are in software, in which case the license you're looking for is Creative Commons By-NC-SA.
If I did want to release a project as open source (not free software) under "free for non-commercial use" terms, what would be a recommended license? AFAIK none of the common open source licenses target this.