I've only set up my hammock a couple of times so I cant comment on the tarp getting in the way, but I have noticed that a combination of my short reach and the trees being quite far apart has meant that the hammock suspension is a bit lower which puts more tension into the RL.
My SL is a 2.2mm Dyneema from Whoopieslings and is good up to 650lb. They are designed to keep the sag constant whilst the suspension angle changes, so the tension in the SL is expected to change from hang to hang. When I set mine to 83% on my last hang it was also guitar string tight even with my tree straps as high as I could reach.
It worried me a little but I've since convinced myself that it would be impossible to get a constant tension in the RL without adjusting its length each hang, and that goes against the reason for having it there in the first place.
Hope that helps.