Staying in Mt Koya

I'm having a hard time picking a shukubo to stay at in Koyasan. There are a lot of options that seem similar, which I think is what's making the decision difficult to me. Plus, all seem to have positive/negative reviews, so I don't know.

I will be going there in September with my husband. I want to stay at a temple that actually feels like a temple and not just a hotel. My biggest fear is staying at one that's just for tourism, if that makes sense. I hate to use "tourist trap" but you know what I mean?

Does anyone have any suggestions?

Ummm, I went to Mt Koya to stay for 1 - 2 nights in a temple accommodation some 5 years ago. I just picked one (dont remember which one). And it was really nice. But Koya-san is quite small, so I dont think there are temples that feel like hotels.
So I guess I would just go of the pictures you are shown. If they have beds instead of tatami & futon, then stay away from that (it would probably just more feel like being in hotel).
The one we stayed had one of the best tofu (actually THE best tofu) I ever ate.

We stayed at Fukuchiin in March 2017 and really enjoyed it. The staff's English is good too if that makes a difference.