No Land Beyond:

Bolt actions speak louder than words.

• Private Eye: Optical zoom length is increased while crouching.
  
• Snapshot: Aiming this weapon is Incredibly fast.
  Lightweight: When held, this weapon grants +2 character Agility.
  Flared Magwell: Reload this weapon even faster.
  
• Thunderous Echoes: Increased damage and firing speed per consecutive Precision hit. Shots from this weapon will knock enemies back.

-Private eye is not found on any Legendary/Exotic sniper, but it fits here, since it gives players control over zoom level, rather than the mandatory zoom when aiming down the sights.

-The ability to stack damage and firing speed buffs causes a risk/reward system that can make this a terrifying weapon in PvP and PvE, and giving the player a tangible reward for his skill. This could be balanced by resetting the buff on a miss/reload/body shot. Alternatively, while not resetting the stack on a body shot, it could lock the player out of adding stacks until he reloads, giving him some measure of mercy since he didn't miss the target.

-Snapshot helps, as players are often using this rifle at ranges less than ideal for a normal sniper.
Flared Magwell can also be useful, since players might want to reload if they miss, in order to quickly start their chain anew.

-Knocking enemies back (Similar to the Sunsinger's Solar Wind melee) serves a few purposes:
It adds to the exotic nature of the weapon without making it overly powerful.
It can push enemies off of perches, capture points, or even cliffs, giving you a "consolidation prize" of sorts for missing a headshot (but it can also push enemies out of your line of sight). And if an enemy is about to melee (or Shoulder Charge) you, you can potentially save yourself through quick reflexes.

*Bonus perks*

-Weapon can fire through shields (Defender bubble, Hive Wall of Darkness, Phalanx shield), adding an exotic counter to things that have too few ways around, and making the weapon even more appealing to use in PvP.
-Ranged Glint. At long range, no glint can be seen, giving the player some safety for long-range shots.
-Due to the heavy rounds, kills from this weapon cause players to ragdoll (similar to kills with a Tripmine grenade). This serves two purposes:
1. It's funny.
2. It can alert players outside of glint-range that there's a No Land Beyond watching that area. This may give them a measure of confidence that adds a small bit of variety to the encounter (I know I'd be juking him to make him miss and lose his stack).