Sitting and reading while you count the dollars someone else is burning through can be rather therapeutic.
You could have said that before in other situations. Regardless of what your work situation is, you can always do this. I haven't but in retrospect realize I could have in more situations than I want to acknowledge. The downside to that is you end up having to live with someone else's decisions for far longer than they spent making the decision, which may often stink. But as an independent consultant you still have to do the same thing. The only primary difference I see is that you usually can see an end in sight when you won't have to deal with decision X, whether it's jumping to another client for the afternoon work, or getting a different contract 6 months from now.
Disengage, then say "let me know by XX:YY when you make a decision" and find something else to work on. Truly liberating.
So I sort of suffer from the same symptoms as the OP. Consulting has proven to be a good choice for me, as I do get some variety and dont get as bored as I did when I was a FTE somewhere...
I think having a niche specialized skill certainly helps, but you could probably find work at a "big 4" firm without it. Being either technical or functional AND personable helps. I am pretty easy going so I can get along with most, and have a pretty positive attitude most of the time. That said Im not overly extroverted, so that isnt a requirement. If you want to do it, work towards making it happen. Linked in(for better or worse) can be a good resource here. Join a professional group there, go to hh events, make connections. I dont think it is a tough field to break into.