Kii Peninsula in Sept by public transport

I'm considering a slow trip counterclockwise around the Kii peninsula this Sept. for my second trip to Japan. I've read that transport is infrequent, sometimes once a day. That's not a problem unless demand means sold out days. Also read that tourist infrastructure all but shuts down at the end of August. That could be a problem if accommodations are few and far between.

I must arrive arrive and depart Kansi airport, somewhere between first week in Sept and first week on Oct. First draft of plans are to take 3 weeks traveling counterclockwise, visiting Koyasan again, and taking the shortest hops I can on bus or train to better fuel my photography habit. I'll travel at the speed of whim, spending as much or little time on Kii as interests dictate.

Are my concerns about availability of lodging and transport realistic?

If you go in the peak season, lodging may be tough to find. August being Obon may or may not be crowded. I think as a solo traveller, you wouldn't have much issue finding a single room. The only issue is whether the place you ended up even has lodging. In short, do not end your day in some isolated region. Some places, like hostels or B&B, may not open if there are no prior reservations.

Useful to know about not opening if no prior reservations, thanks.

I thought my time period was clear in the OP:
I must arrive arrive and depart Kansi airport, omewhere between first week in Sept and first week on Oct[b].

Lodging shouldn't be a problem whereas public transports maybe down to a less frequent run but still should not be a major issue, especially with a 3-week window to explore the peninsula. We visited the region twice, first time for 5 days focusing only along the coast as we used train as the major means of transport. The second time we went for the interior of the peninsula and used a rental car for 5-6 days. So with 3 weeks you should be able to explore the whole of Kii Peninsula on a more leisurely pace. FYI, although we did go for some sites along the Kumano Kodo pilgrimage route we didn't walk the whole route which some people make special trip to the peninsula just for it.

One concern is the weather. Sept is said to be typhoon season and some parts of the Kii Peninsula receive a lot of rain. We read that the town of Owase has the highest precipitation in the whole of Japan.

D'oh!

After reading about climate in Sept., I've decided there are much better times to visit the Kii peninsula. THANK YOU.