I'd use classic diagnosis methods. Separate from each other the various aspects of the system. Remove the chain from the cranks then spin the cranks. Do they rotate freely? Remove the rear wheel from the frame. Does it's cogs (cassette or freewheel) rotate freely? Spin each der pulley. How easily do they rotate? What about the chain? As you run it through your fingers do all the links freely hinge both ways?

Then there's the aspect of which cog/ring combos have the problem. All or just the ones that are cross chaining ones? Are you sure the rear der is staying centered under the cog which has the chain of it? Are there any bent or twisted teeth or links?

All this should take a trained wrench about 2 or 3 minutes to look at. We do this all the time when we take a bike in for service, on the spot with the customer often watching. No rocket science, no curtains or mirrors. Just common sense and basic understandings being applied. Andy.