Keeping the stock tarp should not be a problem. When I was using the stock tarp with my Asym, I never really had an issue with the tarp sagging when I got in the hammock. If you connect the tarp ridge ends to a piece of shock cord and then to the prussic knots, it will stay tight and also give you the coverage you need by staying close to the ridgeline. The shockcord must be fairly stout, long enough to absorb the sag of the loaded hammock, and (at least in my experience) must be on both sides of the tarp ridge. On just one side, it still allowed my tarp to loosen and get flappy in the wind. Shock cords on the stake lines are a must too. They may be stock now but I had to add mine. They will keep every thing snug as the hammock settles under your weight.
...and there came to be a day, all too soon, that I became aware that I could travel no more on my long journey. Though I did not arrive where I had planned, I believe that here is exactly where I am supposed to be...