Slingshot Rebalance aims to fix many of the aspects of slingshot weapons that make them nigh-unusable in comparison to melee weapons. To this end, I've found these buffs make the Master slingshot a useful ranged weapon in the lower levels of the mines, and the Galaxy slingshot more balanced for Skull Cavern.

1. First off, this mod buffs the damage of various ammos. In particular, Stone's damage has been doubled so that the player always has a cheap, but effective source of ammo. Buffs are bolded:

• Default       1     --     1
• Wood         2     ->     5
• Stone         5     ->     10
• Coal           15    --     15
• Copper      10    ->     20
• Iron            20    ->    25
• Explosive   20   ->     30
• Gold           30    --     30
• Iridium       50    --     50
  

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2. Secondly, I tightened up the old damage formula to greatly reduce the randomness of slingshot damage.
Old Formula:            AmmoDamage + RandomBetween(-0.5*AmmoDamage, AmmoDamage)
Nu Formula:             AmmoDamage + RandomBetween(0.35*AmmoDamage, 0.65*AmmoDamage)

So while the Max damage has been slightly nerfed, the Min damage has been significantly buffed. For example, here are the damage ranges for a piece of Iridium from a regular slingshot:
Old:                            50 + RandomBetween(-25, 50)           -->     [25, 100]
Nu:                             50 + RandomBetween(18, 33)            -->     [68, 88]

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3. I made the Galaxy Slingshot purchasable alongside the other Galaxy Weapons from the Adventurer's Guild. It does 4x damage (the Master Slingshot only does 2x damage). I also made the higher level slingshots charge a little faster, so that they can be more effective against ambush enemies like the Dragons in Skull Cavern.

• Regular         0.3s      --      0.3s
• Master          0.3s      ->     0.2s
• Galaxy           0.3s      ->     0.1s
  

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Slingshot Rebalance is Multiplayer Friendly too! I would highly recommned pairing this mod with Better Slingshots for the Utlimate Stardew Slingshot Experience™.

Installing & Usage:

• Make sure SMAPI is installed
• Download this mod from the files tab and unzip it into your Stardew Valley/Mods folder
• Run the game using SMAPI
• If you feel like tweaking some damage values, you can do so in the config.json file
  

Compatability:

• Works on Windows 10. Untested on Mac, Linux, or Ubuntu.
• Compatible with Better Slingshots, and Galaxy Slingshot Obtainable (though, the Galaxy Slingshot will be in the shop menu twice with the latter installed).
• Untested alongside Enhanced Slingshots, and Free Slingshot.