Roger, you will never find a more diplomatic way of weeding clientele than raising your rate.
If they say yes, cool. your billing where ya need to be billing. If they say no, cool, you are open to bill what you need to be billing.
It's not easy to pass up on a half rate when no rate is offered. But if you keep working for half price, you are removing the need for someone to offer you full price.
In short, to raise one's rate, one simply has to raise it and stick to it.