Why would you be trying to melee them? That's just asking to die. THF's are insanely hard to hit, MNK's can CS and use Emp WS to nearly one shot you, BLU's will stun lock you the moment your within casting range, PLD's will just laugh at you as your won't scratch their paint. PVP is the one place you want to be pure page, stay as far away from the enemy as possible and wear them down over time. If you stay away your basically invulnerable, if you get close you provide them with a chance to use their abilities and seriously hurt you.
Your using sleepga not to just strip shadows, but because it'll buy 2~3 seconds (if they have poison pots) for you to silence / bind / paralyze them. Once you've got those on most jobs won't be able to go on the offensive, ever, you can control the entire fight. Sleep I / Sleep II / Sleepga / Bind / Gravity / Break all work to control the movement of your enemy and keep distance. Paralyze / Silence / Slow server to steal their JA's and prevent them from casting. If they try to use items that will give you even more time to do things, and para can proc on items too. You kill them by siphoning away their HP and MP and leaving them without the ability to actually do anything.
Learned these things while fighting BLU's, who think their godly at PVP just cause they can stunlock anything close and tear it them to ribbons.