Oil sample analysis?
Engine oil analysis is used a lot in aviation circles. The concept is monitoring of the metals found in the oil will provide some warning of excessive wear for engine parts before an actual failure occurs. Each sample report is compared to the last report, to detect an increase in certain metals. When the samples found start to exceed the norm then you had better take warning!
A one time sample won''t give you much to go on re what is normal wear and/or excessive wear. If engine/transmission failure is about to occur I''m sure excessively high levels of metal could give you a clue but you probably need some baseline for what is considered normal vs excessive.
Labs doing this type of work usually supply a sample kit with instructions. As I recall, it took a couple of weeks to get a lab report back...don''t know how that fits into your schedule.
If you can''t find a lab to do the test, drop by the local airport and ask at one of the aircraft maintenance shops. They should be able to steer you to a suitable lab.