I saw the title and my first thought was, if it includes a mechanic to use HP as a resource, it wouldn't work. First sentence, drain the DRK's HP. It wouldn't work.

Even if you do give the DRK a shield equivalent to the HP lost, it is meaningless. The only benefit would be if you got healed more than max effective health, but since the shield is so weak, that will rarely, if ever happen. To put it into context, how long does GNB's shield from Brutal Shell last? To put it in another contest, it is about 5% of your max HP. Since you also haven't mentioned any cooldowns, I'm assuming they will be the same, so you will be spamming Flood/Edge of Shadow every 2-3 GCDs aka, when the last shield breaks. That is incredibly spammy in it's own right.

As for TBN, all it has turned into is a button you use to allow more Edge/Flood of Shadow. It is effectively a HP buffer, so you have a bigger margin of error you can play with, so you can spam more and not care about the weak shield from Edge/Flood from running out. All you need is for the healer to heal you.

As for Abyssal Drain and Carve and Spit, the HP drain on AD is incredibly weak, even considering you can spam it 3 times in a row. As for C&S, it is essentially relegated to the 2 minute burst window, using MP just to prevent overcaping. It wouldn't help in what you envision it to do (ie. Provide a buff to help heal back the HP lost from Edge of Shadow).

There is a reason HP is not used as a job resource and that is it is incredibly hard to balance. You can balance the job around itself as much as you want, but as soon as you add an external source of healing, it throws everything out of whack. The FFXIV equivalent for older DRK's HP Drain is to use MP instead. It is all based on the DRK's kit and so it's effectiveness is based solely on how you play the job and not how well someone else can heal you.