This is what I preach in my articles about freelancing. Clients need to enter your frame, not the other way around.

We have a culture that defaults to thinking of freelancers as desperate or they could do cheaper overseas.

That's fine. Allow them to think that. However, when they see that you have an empire with people constantly seeking you out, they'll join the fold and conform to your pricing.

"My project was done by the wonderful [insert your name or brand here]!" Not the other way around.