You can set your custom (fourth) view to "4 Weeks", which does the trick for me.
I have my custom view set to 3 weeks - but the same principle - it shows me from today (or rather, the Monday of the week that today is part of) through to Monday 3 weeks away. It cares not a jot for where I am within the month. Setting the custom view to any other numbers of weeks will doubtless provide the same 'sliding x-week window' view.
It gives an x week window offset by n*x weeks.
So you can see now through 3 weeks, and 3 weeks through 6 weeks. But I want to see 3-4 weeks of window and slide by one week!