First, regarding the TA work, if the work was done full-time and was compensated separately, then it would be considered regular employment. If it was part of your doctoral stipend, then some schools wouldn’t consider it regular employment. However they define it, though, they will understand its importance and its role in your education and career. Keep in mind that the adcoms view your application holistically.
One factor that will have significant bearing on your competitiveness is the quality of your work experience. The "what" looks good, but adcoms will also look for a track record of specific accomplishment and impact; they want to see you excel professionally relative to accomplished peers.
Overall, I think your list of schools is on target
. Depending on the quality (as noted above) of your post-school work experience, they would be in the on-par to reasonable-reach range.
Senior Advisor, Accepted
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