Wow, 5X! I have a small consultancy and most engineers are surprised to learn that 2X is typical. I do know some of the large management consulting firms have very high margins, especially on junior programmers, which you're clearly not. Specialist knowledge will also raise rates. But I suspect they have high churn with abuse like that.

Do they have an awesome sales/marketing team, or are those rates typical for your industry? If it's typical, you might consider freelancing. Or finding a small consultancy that will treat you better and take care of sales for you.

I'll say I was once unhappy and asked to be laid off. They told me no, essentially because I was a cash cow. You think your bargaining position is tough, but if your utilization rate is 100% and their margin is 80%, if you leave they are guaranteed to lose at least 160 billable hours (up to 480) while they replace you. I'm assuming you're not in gaming or a glamour industry where there is a line out the door to replace you.