The cost to have a good quality paint job done by a commercial autobody/paint shop might make you wince. But before discarding the idea, you might want to give a couple of places a call to see if they've done that kind of work before and what it might cost.
Another potential item to deal with if you'd go that route would be 'color match'. You'd probably need to take something or some part of something into the shop that's already the color of bisque you have. They can match the new paint to that. Otherwise, you're liable to wind up with a fridge in a bisque that's different from your other appliances.
Or as jblum offered, maybe consider stainless as an option, just for the fridge. It won't clash - it might turn out to be a good complement what appliances you already have.
Bill