Inverted Cone Cap good idea to prevent staining on outside of chimney?

SweetLife

I just spent a ton of money to get my stucco chimney repaired and restuccoed. I've had an ongoing problem with brown/red staining on the outside of the chimney, but had to get the repairs done to prevent leaks. Now I have a beautiful new chimney and the stains are starting again.
See my prior thread regarding trying to determine the cause of the staining: discussion 151890. After many discussions with chimney sweeps, oil company, maintenance company - bottom line seems to be that the higher efficiency oil burners that run at a lower temp with the stainless steel liners can led to the sulfur etc condensing when hitting the chimney cap and dripping down onto the top of the chimney and running down the sides.

SO - I'm looking into an inverted cone cap that directs the condensation back into the chimney to be burned off. Good idea or bad idea?