I feel that for the melee Inquisitor, you need to have an option which is to simply hold the shield up in front of you so you can actually use it as a shield and block incoming fire
What about some kind of rocket pack shield charge? Reflecting damage back at the attacker might be good too.
With regard to making the cover mechanic redundant for melee characters, from my experience it already is. You can hide for a while, but if you really want to fight most guys you have to move out of cover, close the gap and fight them toe to toe.
It depends on your build. There is this one node which reduces your CDs(the ones that are longer than 3 seconds) by 1 second when hit. This is pretty useful for melee chars since they get hit a lot. It almost allows you to spam the AoE shield skill, but unfortunately the node didn't work correctly when I tested it(only worked for the 20-30 first hits or randomly).
While this sounds interesting, I think it would just be too op. It would make the cover system redundant for melee chars. I think the whole deflect mechanic alone is pretty strong and in a good place right now.