Lets see, well that drive bay PSU your talking about puts out 250 watts on average. Your video card requires 400 watts minimum. Your current PSU puts out about 300 watts or more I believe, but not much more than 300. I'm gonna go with EVGA on this one and get something that puts out more watts for my PSU in the PSU bay. If your looking for installing a PSU for an easy install, well installing a Drive Bay PSU is just as easy as installing a new PSU for the PSU bay. There wouldn't be a way to combine the two PSU's to come up with 550 watts.
As for your system putting out alot of heat, that is extremely dangerous for not only your new video card, but your CPU as well. We're going to have to mod some cooling into your system if you want your CPU and Video card to last.
(yes I am considering video card manufacturers set a high bar for PSU usage, but its like this, better safe than sorry, why else would they put those requirements on the box.)
For the cable, I would buy just a regular male to female PSU extender and connect the male/female to the cables male or female connector, thus longer cable.
For example heres the PSU cable and below it is the PSU extension and below that is your cable.
PSU>O------------Female <PSU Ends as Female*********************
***************+ <connect these****************************
***************Male <extension ending in male*************** ********
****************l ***********************************************
****************l********************************* ***************
****************l<extension cable***********************************
****************l ************************************************
****************l********************************* ****************
**************Female****************************** ***************
****************+********************************* ***************
**********Female Male*******************************************
***************Y <PCI-E connector Cable ********
****************************+
**********************PCI-E Connecter
****************************+
************************Video card
Now if you wanted to do it the other way around your PSU would end in male and you would flip the extension cord over in the diagram and use the female connetor of the PCI-E cable.