It is safe to assume that your phone, on Android 4.x.x, has the stock Brick Bug kernel. This is why I favour the CF-Root method as chainfire's CF-Root kernels have the anti Brick Bug.
As it says in that other method, in step #1, "To get temporary cwm (to make nandroid backups...) or if stock recovery gives you a signature error, follow the next more universal steps.", you will need to implement step #2 if you wish to have CWM Recovery installed, (recommended). I have to confess that I have not used this method myself but a few posters have.
Something else you could consider is flashing a stock Samsung ROM, including a stock kernel, that takes you away from the LPH, storage problem, kernel and then root your phone using the new, stock. kernel details.