I've been working on the order of the second round of bosses, and I'm stuck.
Even though Napalm Man is quickly killed with Pharoah Shot, I don't think it's faster to start with him because there are 3 parts on the first half of his level where Rush Jet could be useful. Also, since Charge Man might be killed faster with the Mega Buster anyway, this might be the fastest route. The only other place I see where it's useful is in Crystal Man's stage, when you're waiting on the lowering an raising platforms. Oh, and Napalm Bomb looks awesome on Charge Man's level and seems pretty useful against the robot chickens. I don't think this is reason enough to keep the route the same though.
Here is a picture of what I was talking about in Napalm Man's level. Where it says "jump" is where the trick shown in Nsm's movie (slide jump in Ring Man's Stage) would be used. I'm not sure if you can do it on the first part of the first picture, so I drew up two routes.