Pull up slightly and then press - this may help the pressure.
I purchased a weaker compression spring from Century Spring, part number 72144S. Now I can push the flap handle button in with my little finger. I was worried that the new spring is a little too weak. But it seems to lock into the detents OK. Century has a slightly stronger spring, part number 72160S which is still weaker than Van's spring VA-114.
http://www.centuryspring.com/
You order must be at least $40. That will buy you 4 springs. Maybe you can sell the extra to other builders.