Using a torch to burn the seeds seems like a good idea. Good luck and hope for the best.
I'm thinking that tillilng the soil to bury the seeds will only delay the problem. Buried seeds will come back to bite you later.
Additionally, if you spread a pre-emergent (such as Preen or corn meal gluten) you can stop the germinating seeds from surviving. Apply it again in 3 weeks; repeat a few times as needed. As long as you are planting plants and not planting seeds in the garden this will work for you.
https://garden.org/learn/artic...
https://garden.org/learn/artic...
