Sounds like you've already tried plenty of productivity apps, but in case you haven't tried it, I've found Todoist quite good.
The "Apple-ification" as you put it is done pretty well. In place of drag + drop to set a time of day, tasks can be created with inline date parsing. So tasks can be created with something like: "Meeting with Tim at Tues 3pm", and it'd pick that up. It's missing direct support for habits aside from having recurring todos.
If you'd like, I've got a 3-month premium code left over I can send your way. Not affiliated with them, just a happy user.
The difference is that those apps use time blocking (e.g., block out an hour for a task in the middle of actual calendar events) and are usually automatic in nature. The ideal system blocks out the time for a task -- it's not just setting a due date.
I too have tried most if not all of the tools in @renaudg's post and have come to the same conclusion: nothing really matches Timeful.
The "Apple-ification" as you put it is done pretty well. In place of drag + drop to set a time of day, tasks can be created with inline date parsing. So tasks can be created with something like: "Meeting with Tim at Tues 3pm", and it'd pick that up. It's missing direct support for habits aside from having recurring todos.
If you'd like, I've got a 3-month premium code left over I can send your way. Not affiliated with them, just a happy user.