a number of people have reported trying sliding knots for adjustment, either to control the length of the suspension rope in an ordinary context, or to attack the hammock to a long single line such as you suggest. The sliding knots on a rope to essentially create a loop (rope on itself, looped around the tree) tend to either slip or bind up after tension. For prussiks to work you need for the rope to which the prussik attachs needs to be 50% fatter than the prussik itself. For your solution that means a pretty fat single ridgeline, because the "narrow" prussik cord has to be strong enough--read fat enough---to support body weight.
Structural ridgelines don't have to be so strong, so the combination of a structural ridgeline to get a defined sag and heavier duty suspension rope to the trees is an overall lighter solution.
What I (and others here) have done that is closer to what you are suggesting is to put rings on suspension rope, with the rings spaced at the distance to define a sag, then connect the hammock to the rings (with rope of the same diameter as the long suspension line). This is heavier than the solution with a lightweight ridgeline, but has its own attractions (which in my case are particular to the DIY hammock I use).