Just a few thoughts...take or leave them as works best for you.
I once spoke with a Mexican reader who worked one of the big markets in Texas. She told me she handled it by stopping with tarot and instead taking out the Naipes (Spanish playing cards) and reading with those. Because the sitter was not familiar with those they would be quiet and listen.
Earlier in the thread someone mentioned doing an Oracle reading. That should be helpful in a similar way by moving the reading to a system they do not know. Just switching to playing cards would do it too as the Mexican reader did.
Another option I have used is Psy-Cards. You can find these on amazon and the website
http://www.psycards.com/ . You can see the cards on the website. Take out the direction cards, the North, South, East, and West and the Yes and No cards. Just remove them from the deck as they get in the way with this approach.
You now use a method that can also be used with tarot and would work very well with the type of sitter we are speaking of in this thread. Have them draw out three cards face down. Now turn all three over.
You ask them two questions. First ask them which card they are most attracted to. Let them think as long as they want. Then ask them which card they are least attracted to. Arrange the cards so the one they are least attracted to is on the left and the one they are most attracted to is on the right. The remaining card goes in the middle.
The one on the left that they are least attracted to is where they are coming from. The one on the right they are most attracted to is where they are going. The one in the middle is a tool or resource they already have that will help them get from the past to the future.
At this point just let them do their own reading. You don't even need to know their question or what the cards mean to them. You will see the light will go on in their head and your reading is done. This is fast and easy and allows you to both deal with a difficult sitter and get them moving on their way quickly.
This can be done with tarot cards too but my experiences have been with the PsyCards and this has never failed me. Difficult sitters are very rare for me but I use this approach with the PsyCards whenever I think it is right. It is a fast reading where you don't need to know the question or what the cards mean, you just guide them. It is also useful in situations where tarot may not fit.
You can practice the approach at this site...
http://www.deceptionary.com/tutor-psycards.html . You cannot physically re-arrange the cards but this is easy to do in your head. Try it with questions of your own and see how this works.
Finally we should consider why the sitter is being such a pain. Though they are quite irritating they are doing the best they can with the brain and emotions they have at the time. Also remember that people project what they lack. In this case the sitter wants approval from a reader that they are smart about tarot. Saying something like,"You could do what I do and do it well" works well with these types of people.
Of course you deserve sanity too. Once you have given them the recognition they are craving switch the reading to an oracle or other system they are not familiar with. Finish the reading and then decide if you wish to work with them again.