One method would be to put index finger on one side & thumb on the other, almost like you're "cupping" it, and then push IN with regular rhythm. Yes, if you roll it around, you might get some out, but if you're trying to get out a LOT, then you need to really hit those reserves back in the ducts. And if you can FEEL that you have a lot in the sides/near the armpits, then try doing the push in with index/thumb with one hand, and just actually PUSH on the full part with the other fingers of other hand.
That being said, I have had great success with a pump. They are not scary at all. If you're trying to "stock up" on some milk, then why not use the quickest way possible - it's not like we all have tons of time on our hands. Self-expression has been very challenging for me, too - even when trying to express just an ounce or two for mixing with solids - and even when I know I am "full".
Big advocate for breathing in, calming down, drinking some water/fluid, and just relaxing to let it happen. (this helps with pumping too)