To answer your second question first you do need a running line to use a shooting head. Unless your casting is at a high intermidate or expert level I would stay away from the use of shooting heads all together. Even the best of them hinge at the connection to the running line.
As far as what type of line to go with next I would stick with what you've got just use weighted flies to get you deeper.
You say you fish waters with moving water most of the time so even a quick sink or depth charged line are rendered almost useless unless you cast up current giving the line time to sink properly.
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