New 20amp circuit via old conduit or not?
Here's the good news. You have figured out two methods of running your new circuit and both of them work. As a DIY'er probably the best method for you to take would be to run the 12/2 to a new box.

As an electrician I would look at trying to run the conductors in the conduit. The magic number is 40% fill for the conduit and boxes. So you would need to know the number and type of insulation of each existing conductor and the size and insulation of the new circuit. Once you have that information you would need to go to the Table section of the NEC and run the calculations to see if everything would work.  Also you would have to determine how you were going to make the transition from the existing circuitry and feed over to the new receptacle. This seems to me to be a little overwhelming to someone with limited experience.

So I would suggest you use the old KISS (keep it simple stupid) method and just run a new circuit. The only reason I would think about using the conduit was if it became really difficult to run the NM.

Hope this helps and good luck.