I have never seen or heard of UPS providing a time frame for delivery (other than by the end of the day) unless it is a next day air saver or something else time sensitive. I am a UPS My Choice member, too.
In my neighborhood, there is a UPS truck that rolls through any time between 10am and noon (the time sensitive deliveries) and the main delivery truck normally gets through our area between 4pm-8pm. Typically though, my area is on the last leg of our UPS guy's delivery track, so it can get kind of annoying.
I would suggest trying to see if you can change your phone to Will Call pick up before it gets on the truck for the first delivery attempt. That is what I did, and I plan on picking up my phone at a major UPS hub at 8am before work. Your options may vary though, depending on what the closest option is to your home.