When I returned to my silk scene I realised that I forgot to untick 'opaque' on the silk - which is why my previous test did not have softened edges. Unfortunately it is quite hard to see the softened edge in the test animation since I had to keep samples low. In my still renders, though, I'm confident enough that it'll look alright. Luckily this shot doesn't have as long of render times as my previous entities, so if I have to re-do it I can.
I also attempted to adjust the lighting so the slight ripple at the beginning of the animation was more visible. However, I was unable to do much in regards to this without changing the lighting too much. Since the silk is white/silver and the lights are directly above the silk, the fabric is pure white even with a slight wave to it. I'm willing to compromise on this, since any tests that got me close resulted in the fabric looking odd later in the animation or the lighting looking too different compared to other shots. If I have time that'll be something I can go back and experiment with more. I also adjusted the bump map I was using to give the silk the slightest hint of fibrous texture to scatter the lighting.