Since it takes 3-4 minutes now to fill the tank and washing machine, I think you have a pump problem or a leak fer sure... it should not take that long unless you have a very large pressure tank, or very small pump or a deep static water level which the pump can't move water easily from.
But I am glad that I finally have you thinking.
You could have a leak that doesn't need more pressure than the weight of the water but you'll find out quicker if you remove the check valve and use water and let the pressure push against the pump's check valve at your cut-out pressure setting.
Click Here to learn how to correctly size or program a water softener.
CAUTION, as of Nov 12 2013 all YouTube videos showing how to rebuild a Clack valve have an error in them that can cause damage.