So I set out to mod Minecraft version 1.12 to accomplish three goals initially:
Revert the combat system back to what it was in 1.8
Make it so the gold pickaxes are on the same mining level as an iron pickaxe instead of on the same level as a stone pickaxe
Make it so cave spiders spawn in caves naturally under y=30
However, as I learned after searching a couple of forums posts where people wanted to accomplish similar tasks, it seems that altering the base game through modding is strongly discouraged. Even so, is there a way to change or implement any of the three things I wanted?
No, it is not discouraged. In fact it is highly encouraged. What you read was about the method used to change the vanilla systems. Modding is always about changing the game, but it is supposed to be done in a way that is friendly to other mods. So Forge creates a system of "hooks" which are ways to change vanilla in a way that is more compatible.
One of the main way Forge allows changing of vanilla is the use of events. For example, you can handle the PlayerEvent.HarvestCheck event to change the gold pickaxe ability to harvest things.