Good question--I am not sure what I would do about the chickweed and henbit. Both are winter annuals--so--in theory--they should die when the temp hits about 85. If the weather is dry and the fertility level favors rapid growth of the grass--a short cut should encourage the chick and hen to fade out, as you let the new grass get longer. A shot of herbicide wouldn't hurt anything really.
You can always seed it with the understanding that on average, it will take three times to hit a lucky stretch of weather. Is there likely to be a crabgrass problem?