Are you sure its not the front ring thats 24 and the rear cassette that 29?Switching to a 24 tooth rear cassette would be odd as most are at least 28 and on websites you can get them up to 34 tooth for around $20.Maybe you could have him special order one of the touristo specials from
www.sheldonbrown.com .As to the downtube shifters I have always had them on my bike and they are fine for touring needs so if you don't have racing asperations I don't think they would be a deal breaker if that is what it takes to get an economical bike.Others can better comment on what all would be need to swap out shifters though.