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Actually I think Jitter Nodes should get you pretty close. Did you use the Add Nodes extension before using Jitter Nodes? I don't know the scale of your example, but the more nodes you have, the closer you'll get to the example. If the example is at 100%, I would guess 30 to 50 nodes along the left side of the L, might work. Also, be sure and check the node handles option. That will give you an even more random and more wild of a jitter.
Oh, and also, the black border -- is that a single, simple path? I think you'll want to take that single path, and do Path menu > Stroke to path, first. Then add nodes, then apply the jittering. I think you'll get really close.
And another idea, although I'm not sure if it would technically fit your "all vector" requirement. What if you found a font like that? Then you could simply use the Text tool. What I'm not sure about, is if text is vector. I'm guessing not. BUT even so, you could use Path menu > Object to path, and then it would be vectorred! Just a thought
