Clay drops are so bad that we need to follow this route to upgrade our city:

0. Create new realm, use same character, run and ignore enemies if possible, skip all cutscenes
1. When you open first gate with lever, dig a hole just after you exit the gate (to the south)
2. Another dig site which may drop clay is to the south by the road, an indication would be first boss roar
3. Check merchant, he may have some clay
4. Go to the rookery, have free ichor (or don't), then rush to the merchant again and check if he has clay
5. (Optional) If you really want one more ichor, take Within Our Walls bounty and kill miniboss in war room
6. Repeat