Instead of the 6pc having a healing power why not reduce or delay the penalty for missing shots from the 4pc.

Example:
currently: 4pc stacks 1% extra damage/hit, -2% for miss, -1%/sec

6pc options:
only -1% per miss
- or -
immediate buff of 10% and then is impacted as normal
- or -
no loss for missing next x shots (10? 20?)
- or -
immediate buff = FA/1000% (so 7000 FA = 7% buff) and no reduction, just a nice buff to damage based on taking the entire classified set

Just some thoughts.