Here's a UI concept:
Every day, it shows me the standard 9-5 "time grid" of 30-minute blocks. Maybe it would show them a week into the future too, like the 'week' view of a calendar app.
Underneath, I'd have my stack of TODO items. Every morning, I would drag a few items into the blank spaces on the calendar to plan my day. Then, I could check things off as I finish them. If I fall behind, no bigs: just drag the old items onto tomorrow's time grid sometime.
I've tried to simulate this with Trello. That's a great way to get the 'TODO' part down, but it isn't so great for planning my time.
I've tried this with Org-mode. This really comes the closest out of all of them.