Blimey, can't see how worn tappets would cause a car to cut out, and yours don't even seem to be worn, are they faulty in that case? 27k miles after overhaul, or total life?
Engines don't usually suffer from high oil pressure, your mechanic is thinking of middle aged golfers, the oil pump has a relief valve but that is more prone to sticking open causing low oil pressure. The tappets are pressurized by oil pressure, but that is only testable off the engine.
If the problem is your car cut-out, then you should be looking at the fuel and ignition systems - a V8 would go on forever with worn camshaft/tappets etc, probably only do 10mpg, but it would still be running.
Need more info.