OK, I think I am making this harder than it needs to be, but here goes: First day of trip is Sunday, January 24, 2016. I live in Arizona, I try my ADRs at 3am Tuesday morning, right? Thank you oh wise ones.
http://www.wdwinfo.com/wdwinfo/dining/pscalc/dispscalc.html So according to this your 180 date is July 28th. It will open up at 6:00am eastern daylight savings time.