Boa will do the job – does it have to look like a rope? The indents at the edges might be tough where the grooves between wraps are. I haven’t tried this but you could make a copy of your main “rope” and increase the spacing and make this second rope a little smaller so the “balls” of the brush that makes the shape of the spline barely overlap are the width of the first rope at the edges of the balls only. Use this second spaced rope to mask out the first boa object – when you get the spacing right it might line up with your rope wrap texture and voila, edge bumps.
Depending on how you want the ropes to move (other than just growth along their length) you might have to combine boa with a few other scripts available at the same place to get proper easing control of the spline control points.
And depending on your realism requirments you may have to cheat to get the overlap shadows by adding a masked soft or hard edged element within the rope shape itself.
Doing this in 3D would be easier but unless you want to go with a collision dynamics system you have the whole problem of intersecting geometry which can detract from the realism – shadows would be solved but again you have the issue of point level animation for the spline points. But you can always conscript some nulls and animate them and have their positional data control the spline points. This will give you the easing you can’t get from PLA.