BAS - while that solution did work, that would require me to create a new layer solely for the walls that shouldn't intersect, and that can get rather messy pretty quickly. I'll use this method if all else fails, as it appears to be the easiest solution. Thanks.
Peter - priorities don't seem to be working in this situation. They're the exact same wall type, a simple composite. If I uncheck 'Enable Wall Priorities', then they still intersect, though it looks like the following attachment rather than the first attachment. Moving the wall slightly back isn't an option.
Appreciate the help, and hopefully there might be some other suggestions out there.