Any ideas? I was thinking a thick mulch smother left on the area for a month or so, then start over with new lawn planting. I thought rototilling would just divide the roots that would spring up again later. I don't want to use chemicals.

The infested area is app. 300 sq. ft. and almost 100% violets. Any ideas on how restore this area to grass?

I would use a heavy mil black plastic to kill off the violets. How long to leave it on would depend on conditions, temperature, etc. In summer, a month might work.
Then rototill and level the area.
I would look for a pre-emergent also so that seeds do not sprout.