Ah, and now we're at a point where we're conflicted on what comes next.

The altercation happens when Goshikuro is fully recovered. Kurama's rage only speeds it up, that does not mean that it is complete. It is complete when we need it to be. The fight between them is meant to be on a scale as large as Yusuke fighting Elder Toguro, so it's definitely a 'final boss' thing. Kurama still has to make certain that the demons within his school aren't still manipulating people into suicide. 

It's a risky choice, but if he cannot find an alternative then he'll have to use that power to disintegrate whatever hold her possessor had on her. It'll be a brief transformation, nothing super dramatic. There are things in that form he cannot accomplish in his base form, and were it not for a couple perverts he wouldn't have found Botan in time to save her life. 

We can do two henchmen. Kurama does not want to act unless he can corner the demon in question, because they could just leave the body that Kurama beats. So they'd need to find some way to entrap them. They put Botan in danger. Shiori isn't safe either. So yeah, they may need Genkai's aid to help secure his household and the school for the time being, at least until those two demons are dealt with.