Over-seeding lawn

Our lawn is full of thatch.  We have already scarified twice and filled two of those huge builders bags.  There is still a lot of thatch patches which are like thick straw.  My instinct says we should scarify until we can see bare earth, but my husband thinks we can sow seed as the lawn is now, having removed a lot of thatch.  We are going to aerate then get top soil and lawn seed containing feed to spread over and then roll in.  Some dips in the lawn need leveling out too. Advice please; sow with bare earth showing or when there is still a lot of thatch?  My sensible side says get down to the earth so the new seed has a better chance of germinating, but I don't want to waste time and effort if the new grass will grow just as well with some thatch still in place.  (Can't put a photo on, as I don't have access to a mobile phone that can download a photo).