St Augustine yard - dead areas

I've got about five or six small dead areas in my St Augustine yard. They vary from one to 3 feet wide. They are very big spots.

I'm pretty sure it was sod worms that killed it. I've thrown out insect killer in the entire yard and removed small weeds from the dead areas. No signs of worms and it's just dirt right now.

Any suggestions on what I should do to grow grass back? I'm thinking the obvious is to till then lay down some St Augustine sod.

Also considering till dead areas and throw Scott's turf builder seed on it. Or till and leave alone hoping St Augustine will eventually grow in.

Thanks for your time!