Should I add 2x8GB RAM sticks to my existing 4GB sticks for 24GB total?

Yes, add the 2x8GB and keep the old 4GB sticks for 24GB total. Mixing different capacity RAM sticks isn’t ideal, but it usually works fine. You might lose dual-channel mode for the 4GB sticks, but the extra 8GB of capacity will benefit you more than the slight speed hit in most real-world tasks. If your board supports it, you’ll have asymmetric dual-channel, which is better than nothing.