Rewards are once per week, per class. You may have found a loophole last time by picking up the bounties on all your hunters before turning any in, but this time, by turning them in on one hunter, it counts them as complete for all your hunters, as is intended.
There is no benefit to having more than one character of the same class. You would be better off deleting two, and making a warlocl and titan, and playing them as well, as you would then have three time a as many powerful/pinnacle rewards each week.
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And I thought I finally found a partial solution to Bungie's terrible game design. Time to hope this never gets patched!
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Or just don't play. If you find the game design so terrible(like many others, myself included), don't support them by playing. Playing adds to their numbers, not playing subtracts from them. Smaller player count=less money for them.