Modify 3-way switch to add circuit
Color coding time

Cables have certain default colors of wires.  We're married to that, so usually trying to "color code wires by function" is a big mess.  But in this case, it works out to be very close. Let's get there. 

I want you to mark both traveler wires with yellow tape (or another color, just not black, red or white).  No need to distinguish  one from the other. We wont be doing anything with them; I just don't want to confuse them with the wires we will be working with. 

Now, remove the switch that is going away.  When you do, you will free up a "pigtail wire".  Remove it from the black bundle (always-hot).   Tape or paint it red.  

With the travelers marked, there is one red wire on the 3-way switch.  Remove it and replace it with the red pigtail. 

I believe at this point you have three red wires, all loose.  These are switched-hot.   Join them.  

And we're done.