I'm actually at a point where I'm planning to refuse a raise next year because as my hourly rate goes up (I work for a consulting firm) I get priced out the work I most enjoy doing. I am increasingly forced to delegate more of the writing work I enjoy and do editing and management instead, which I enjoy a lot less. I switched careers almost 20 years ago to get out of management, and don't want to get back into it now. I've already refused several offers of promotions, so I've been officially taken off the "career advancement track" and given a new job title, but now I'm going to be even more radical and refuse a raise. But it makes sense for me; I'd much rather stay happy than earn more money. They pay me well enough that I have more than I need anyway.
I completely understand your situation and I think you're making a smart move.
SIDE NOTE: By refusing a raise, wouldn't your employer just raise the billable rate and pocket more or does it not work that way?