Assume a mass casualty type situation. Something along the lines of AR-558 with physical wounds ranging from phaser and disruptor hits, to concussions, broken bones, and the like.
Each Chief would be from roughly halfway through the run of their series with whatever knowledge and experience they had at that point. Each would have access to whatever kind of portable medical kit a medical officer of their time would have brought for such a situation. There are no able bodied personnel to help. No they don’t have access to a transporter.
Reno did pretty well for an engineer when she kept the Hiawatha crew alive. She didn’t really treat any of them, but she approached the situation from an engineering standpoint since the body is basically a machine, and she kept the machine running.
Of the ones listed, Scotty and O’Brien would be the most likely to just store the injured in the pattern buffer for later, proper medical treatment (like Dr. M’Benga did in SNW), so I would say they would perform the best.
Edit: Didn’t see your transporter bit. I still think Scotty and/or O’Brien would improvise something along those lines and solve the problem with the pattern buffer.
I’m specifically disallowing the transporter trick because the scenario is about making them provide treatment. Same thing as making sure they don’t have any able bodied help to divest responsibility to.
Consider this a tuned holodeck training designed to diversify their skillset.
The Kobay-ouchie Maru.
How do you like my solution?
The alien blood corrodes away the bottom of your cup. Now what do you do?
I try to communicate with it.
It speaks only in disposable cup idioms. It says: “Red Solo, when the beer fell.” Now what do you do?
I eat the cup so that I can have its inner light.
You arrive without traveling, see all without looking, and do all without doing. You get a nifty flute souvenir. The ship explodes. Score: 0/100. Thank you for participating in the Kobay-ouchie Maru.