avoid using 20 pin to 24 pin convertor. it does not make sense electrically speaking.
if ur rig is working fine continue using it as it is.
depending upon the "effort you are prepared to make", or your modding skills you may
1) mod ur existing psu wire harness. (i have done it cheaply and effortlessly on my powersafe 500W)
2) buy a new psu having atx 24 pin connector as well as dual 12V rails and other connectors as per ur requirements. (preferred)