And better yet, is there a way to trace through the nodes from endpoint to endpoint to see how many "jumps" a transaction has to make before it reaches from one end to another?

It would be something like X = N/(8^X)... I think.  Where X = number of hops and N = number of nodes.

So say we have 50,000 people with nodes running.

X = 50,000/(8^X)
X(8^X) = 50,000
Uh...

It's been a while since I took a math class.