JRickW I agree with your plan.
I understand you only have soot coming out in the exhaust water and not black or blue smoke? The soot is probably just being washed out of the exhaust system and is inconsequential.
If you don't have dark smoke the engine is not overloaded so I come back to being starved for fuel. As Faster says we can't tell a good injector by observation (but sometimes a really bad one). I would pick up a new one for your next troubleshooting session too.