I help design and develop new products through Zalaco.com. I also help teach other people how to launch and operate their own small lifestyle business.
I love creative methods for billing.
Yes! You can certainly bill by the week, explaining that your time commitment during the week is actually 5 half-days. Why not? It's a clear system that's easy to understand. You can refine/iterate the details as you go forward.
This can help you build clear back log (as clients book in advance) and has the potential to create a very stable income stream. If there's a cancellation or you have an empty week, you can easily market that availability as a last-minute discount to you existing client base.
It also has the advantage of creating scarcity. When your website points out that you have ZERO availability until 6 weeks from now, that gives you credibility.
It also reserves time each week for you to do overhead and business development stuff (such as initial consults with new leads).
This kind of block scheduling certainly won't work for everyone, but I see many advantages if it does mesh with how you work for your clients.