I've only learned about SSS today after reading this thread so I may have it wrong but...
I think you have your nodes set up incorrectly in that you have your subdermal image feeding into the color on the SSS node. The color input should be the surface color:
The subdermal image should feed into the radius input on the SSS node, and represents the fraction of the Scale value distance that light of the respective color (RGB) can travel through the material.
Here is a simplified node setup for illustration purposes:
The primarily red radius input means red light can travel further than the green or blue. I picked this value arbitrarily, it likely isn't appropriate.
The key value here is Scale which indicates how far light can travel through the material before emerging, and is multiplied by the RGB radius values for each color of light. A small value will only affect a small area from where the light enters, a larger value will affect a larger area and may allow light to travel right through an object if it set to a value larger than the size of the object. At 0.025, on a character that is 1.74 blender units (i.e. 1 unit - 1 meter) tall, light can travel 25mm (reduced by the RGB radius values). That's approximately an inch and seems unrealistically large but it may be that light traveling that far would be very dim when it emerges.
A larger scale of 0.075 allows light to scatter all the way through the hand:
So you can get the "only at the edges" effect you want by picking the right scale and radius values, without an internal "skeleton". It might be interesting though to use the actual bone skeleton that Jujube put in the repo if you want to get stark bone visibility. Actually, I'm not sure that SSS models light traveling through an object or just traveling laterally along the surface.
Like I said, that's my understanding from my reading today, use at your own risk. If one of the more knowledgeable people here can correct me if I have it wrong that would be great.
Edit: Btw, I did try your skeleton clothing, I wasn't sure how to test it but in x-ray rendering I couldn't see anything, where normal clothes are visible.