I blame the poor handling on the electric power steering. Once a small, light car is in motion, power steering isn't really necessary. I don't feel the electric power steering does the Mirage any favors in the handling department.
I drove a car that was smaller, lighter than a Mirage for 14 years, and it handled highway driving better than my Mirage. It had narrow 12" tires (145SR12), & it handled perfectly fine. That car (designed by Mazda, built by KIA, sold by Ford) didn't have power steering. Power steering wasn't necessary.
I can't speak for wider tires, but I feel a rear sway bar helps stabilize my Mirage on the highway some (especially on windy days). I haven't used anything other than factory size 165/65r14 tires, but I could see where wider tires may help some with the light steering issue.