CBDunkerson
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There are two issues to consider here;
1: Thrown weapons vs the fighter thrown weapon group. The sling and slingstaff are in the fighter thrown weapon group, but they are projectile rather than thrown weapons. Thus, many GMs will not allow them to interact with 'thrown weapon' options at all.
2: Even if we view the sling and slingstaff as items which are boosting your ability to throw stones / bullets... that might then allow them to benefit from Mighty Hurling, but not from Two Handed Thrower because that feat requires a one or two handed weapon thrown with two hands... and the things actually being 'thrown' in this case are sling stones / bullet ammunition, which are not even 'light' weapons.