For sure--instead, coil them alternating front to back, reversing the twist in each coil by rolling over or under with your thumb and index finger. Stored that way there is zero twist. Un-coil in reverse.When you change heads, do you wrap around your palm or fingers? Done this way without taking the twist out sets a twist in the line every time.
I wish you would come up here and find the A/F 570 skagit head I lost with about 20ft of rio running line this past fall in the 'geen.It seems that I am frequently stumbling upon Skagit head/sink tip combinations in shallow tail-outs. In the spirit of "Think Globally, Act Locally", I try to recuperate these heads as best as possible.