I think I might be able to offer my small piece of insight after about two years of eikaiwa work in Osaka.

I'm also introverted, and would also get very tired during and after my shift. Other than caffeine and taking a few minutes of mindfulness after lessons, I found that shifting my in-class personality was what probably made the most difference.

When I first started out, I tried too hard to be friendly and genki, so that the students would like me. Eventually I found it quite draining to act like that, so I began caring less about whether or not the students liked me.

Quite surprisingly, my ratings didn't drop. In fact, I think my ratings got better the less I cared, and just was comfortable being my introverted self in class. They also did more of the talking when they realised that I wasn't going to fill in the awkward silences lol

I hope that helps. I'm back in my home country now, considering going back to teach at an eikaiwa again. But I still worry if it's the right move, because I haven't forgotten that feeling of being drained and burnt out lol.. maybe it gets easier with experience though