The way you are thinking would be much cheaper than what I'm doing with the downside that clients data exists on the same server (but maybe they won't care) and the fact that a performance issue for one client can impact other clients.

I haven't found an AWS account per customer to be to bad to manage yet and makes keeping track of your AWS spend per client simple. It's also trivial to run your resources in say Sydney for your Australian clients and London for your European clients.