...the pump-style. Not sure if that entails altering the case in any drastic way (which would be bad, of course)--maybe one of the tech guys will chime in.
An all-correct 6240 is worth over $25k depending on condition--it's considered a pretty rare Rolex reference in the scheme of things. Obviously, for one that is completely messed up and requiring a lot of effort to return to spec, $15k doesn't sound like a terrible deal...depending on how screwed up it is.
Does the dial say "ROLEX OYSTER COSMOGRAPH" or just "ROLEX COSMOGRAPH"?
Best of luck,