ML, here's a strategy to narrow things quickly, if you're looking for a convenient Firostephani hotel with a caldera view: Just google Booking.com Firostephani and put in some dates (dummy dates" -- see below) ... and then you will get a list of hotels. Above list on RH is a box "map View" click on that... the map will show blue balloons along the caldera, the ones with red centers are fully booked, the other have rooms -- when you move your mouse across each, it shows the €€€€ rate and the review level (try to get something 7.8 or better). Working with the map will keep you from "falling" for a pretty pcture of a hotel that's waaay back from the caldera view, or way East of the main N-S- road. Anything very much East ( to the right ) of that Road is quite downhill.
Rich, starting so late, is going to have a hard time getting what he wants at the price he wants. but ML, you have ages. Some people in your place try a "dummy booking" search using September 2018 dates... but they won't see many hotels, because they'll be so fully booked. What you COULD do is put in "dummy dates" of Oct 10-13. 2018. Then you'd see a good selection. If you see some you like, you could e-mail the places direct. However, you won't get a response until about Sept. 1 or later Why??? because All August is their Very Busiest Season, they don't have huge staffs ... and are too busy handling the August guests to deal with a backlog of e-mails. Make your wish-list, contact them in September, and you'll have some good choices. Decide if you want to splurge on a pool hotel, or if you're going to be too busy or too short a stay to use a pool... and then you'll save a lot.