How can I trigger other circuits based on specific values of a 12 bit ripple counter?
With only simple logic gates, you're going to be "putting a crazy amount of them" on the four MSBs.  Optimizing your logic can help reduce the number of gates (there are two that start with 11, so they can share some gates, for a start).

However, if you were to spend a few pence and invest in a 74xx154 4-to-16 decoder then the 16 possible combinations of MSBs would be presented to you as one of 16 outputs being pulled low.  Much neater than lots of gates.

If you can't get a 154 you could use two 74xx138 chips and use the highest MSB bit to choose between them.