New Construction: When to start advertising prior to completion?

[Garen T.]

Building a duplex and the current time line has occupancy date on July 6. 

Backing up in the schedule:
Cabinets installed on June 6
Granite installed on June 19
Appliances on June 21
Carpet on June 29.

I would like to start putting ads on Zillow and Trulia in early June, as it would be great to have someone selected and ready to move in as early in July as possible. However, I do know that there are some people who can not see beyond the construction mess and I could lose out on someone. Also, from a cash-flow perspective, it would be fantastic to have the deposits come in during June. But I also know that getting the best tenant is much better than getting the wrong family just to get the money flowing.

I've thought about putting out a post and having the June weekly check-points included. So, that anyone reading the post will know the schedule and decide when they would like to come over. The longer they wait, they may lose the place. 

In my area, this should be a high-demand property. 

Any advice?