Replace HDD with Battery
Buying a new cable from apple was too expensive for that old MacBook,
  so I kicked out the SuperDrive and put my disk in there.


Doing a quick check, this is currently selling for $14 including shipping.  While I'm not against adding a second hard drive, this fix is very much economically feasible to keep your drive in it's default location.


  Considering that the old battery is 8 years old and there is more
  space now it should be possible almost double the battery capacity.
  
  Now I wonder if there is any way to get such a battery?


Unless you plan on building your own battery pack, this is simply not an option.  Your best bet is to replace the cable and battery and simply be done with it.