What camshaft should I use?

Surely it will. If an exhaust lobe is wiped, that cylinder will still fire, but back up through the intake and disrupt everything. If the intake lobe, the engine will skip, and power will be down and efficiency goes out the window. So yes, mileage will be adversely affected either way. Have you had the valve cover off to inspect for a wiped lobe?

I suspect it. I saw a few pushrods spinning but I need to double check. I know that no matter what I do to the car it will have a rhythmic “pop-pop” out of the tail pipe, you can hear an audible drop in engine speed that matches the misfire out of the exhaust, and looking at the engine you can see it shaking when running.