I suppose he's not interested in expanding? (my clients love being overwhelmed... typically gets them giddy for expansion, which for most is a life long dream)
If I were you, I'd try segregating my call tracking lines. I'd test this for a week and send the main line to a REALLY well done voice mail (something subtly indicating "we're on the line working with another client and be right with you" NOT we're too lazy to answer the phone and don't understand what customer service is.... HUUUUGE difference as I'm sure you know.)
Screen/filter the winners and auto email VM to client receptionist. Sell the rest or get creative with a strategic partnership of that company.
This will do two things: A, conversions will drop and screening will go up, usually resulting in higher quality leads which your client will love (** only seriously interested people will normally call back twice, leave vm's, etc...) and B, create a potential opportunity with a sister company, and so on.
Anyhow, just an idea. Now that I think of it, it may not be practical for most businesses/clients that weren't created for lead gen.
** - Normally is the key word here... I've been wrong on more than one occasion with certain industries where tire kickers will call and call and call.., only to price shop their estimates to death and waste everyone's time except for the poor sap that ends up working for them for peanuts.