I wonder how my six years of teaching experience will compare to someone who's "right out of the gate" applying for the same tenure-track job.
Not all schools are like Helpful's, so in a way, you might indeed be back at "square one." Svenc's post clarifies this.
My suspicion is that your teaching experience from before may be part of what gets your foot in the tenure-track door in a tight job market, but it won't count for much beyond that. It certainly won't allow you to apply for anything other than entry-level positions, nor would it allow you to shorten your tenure clock at most institutions.
In your cover letters when you are applying for jobs, you can emphasize your years of teaching experience, which could help to make you a more attractive candidate for teaching-focused schools.
Good luck!