You don't get the Tier 3 Helmet instantly. Normally, you have to do 3 Weekly Bounties and each time you complete a Bounty the Tier goes up (first Bounty Tier 1, second Tier 2, third Tier 3). This would be 12 Bounties in total. To make it easier, you can get the Tier 1 and 2 Helmets in The Reckoning after completing your first Tier 3 Bounty. So once you have a Tier 3 Helmet (like you do), you can grind the Reckoning for the helmets from the lower Tiers and then complete the Bounty after getting the helmets. Then it's only 6 Bounties (3 for initial Tier 3 Helmet, 3 for the other classes). As you already completed your Sentry Bounty for the week, I don't think you can get the Tier 3 Helmet before the next Weekly Reset.
Dang, thats a lot of work. Nice job.