the new lawn?

We had a sprinkler valve fail and our grass was not getting watered for a few weeks, and our kids also play at one end of the lawn more than the other, so we've developed some dead spots. We're in California so the lawn never really goes dormant like it does in colder climates. I decided to reseed the entire lawn to try to get some thicker coverage. I rented a core aerator and first aerated and then reseeded, and then covered in steer manure as a topper to hold the moisture and kept it wet for a couple of weeks.

Its been about three weeks and we haven't mowed or walked on the lawn yet since reseeding. As the new grass has grown in, the new grass shoots are visible but the weeds in the lawn are very evident. There is a TON of crabgrass and another clover-like ground covering weed that seem to be about 40-50% of the lawn now! I know I should have applied the broadleaf weed killer BEFORE reseeding . . . but what's done is done. I want to kill off as much of the weeds as I can without damaging the new grass seedlings.

Interested in any educated opinions on this. Thanks in advance.