"...so am seriously contemplating booking myself at this point."
As others have said, this is generally quite easy to do yourself.
"...we would like to stay in a ryoken on Miyajima"
There are several on the island at very different price points. Something to consider though is, are you going for the full onsen and dining experience or are you just after the dining?
Some ryokan are rather limited when it comes to the actual onsen facilities. I would say that Iwaso ryokan is one to consider, but it is expensive.
https://www.tripadvisor.co.uk/Hotel_Review-g1022438-d325033-Reviews-Iwaso-Hatsukaichi_Hiroshima_Prefecture_Chugoku.html
.
"(with day trips to Osaka)"
If I might make a suggestion, if you're looking more for an onsen experience (not just the dining) there is also a newly renovated ryokan to the south of Osaka in the small coastal town of Nachi-Katsuura.
The Urashima hotel was reopened this year after a refit and they have stunning onsens that are in caves at sea level. So you can sit in the onsen and watch the Pacific ocean on nearly the same level.
On a nearby island there is also the hotel Nakanoshima which is quite expensive but has outdoor onsens almost at sea level.
.
"Do you use skyscanner for flights and booking . Com for hotels or do you go direct?"
As Takoneko said we have also always searched flights on a website (personally, I use Kayak . co . uk) but then book the actual flights through the airline's own website. One advantage I find of doing this is that you can check out more alternatives on the airlines website that may not appear on Skyscanner etc eg with departure times that work better for you.
The same with booking . com etc. I'll look through that to get an idea but then also have a look at the individual hotel or chain website. I've found that often the likes of booking . com only give a basic room but sometimes you can find really nice rooms on the hotel website for very little more, or larger rooms etc.
Below is a photo of one of the onsens in a cave.