How to get another person picked to work with a difficult client?

I'm a mid-career lawyer in a mid-sized firm. I get pretty consistent good reviews, and referrals of more business, from clients.

There is one client, however, who is very unpleasant, and he doesn't even pay his bills, either on time or in full. The client works with my boss (a partner) and me (counsel). He has complained about me over and over to my boss (another lawyer) (in my view, to get his bills reduced), and he has complained about my boss to my boss, but he keeps coming back to me alone; he doesn't even copy my boss on emails.

I can't stand working with him; he's mean, disorganized and is one of the rare few clients who doesn't want to "do the right thing". Since he complains about me, surely it's best that someone else in the firm be the point person for him; given the level of his complaints, I'm surprised that he hasn't left for another law firm.

Would it be unreasonable if I go to my boss and ask to discuss who else in the firm I could transition the client to? It seems like that would be a win/win: someone else in the firm might be able to please him, and the firm's risk of losing the client would be reduced. Wouldn't just explaining that to my boss be wise?

Thanks.