The Chugoku region is crammed full of little known tourist gems that most people overlook and never see. A couple of impressions came up from your plans though.
First, for Aug 20-21, I presume you mean Korakuen?
https://www.youtube.com/watch?v=5zAI3_N7NEMDon't pass up Handayama which is not far away either - very beautiful and wide layout.
https://www.youtube.com/watch?v=JGQ8o7k9GbAFor Iwakuni, the bridge is truly an iconic image of Japan, but not close to the stations - hopefully you will give yourself enough time to see the park and go up to the mountaintop castle. Great views and really nice.
https://www.youtube.com/watch?v=0COOZXi66mMFor Aug. 22, the Kawachi Fujien is a real pain to get to - but are you aware that the wisteria season is late April through the first part of May? If you expect to see the tunnel of wisteria you may be in for a shock. Autumn colours there are very nice too, but August is way too early for that.
Seeing Sarakurayama would also be a great addition - one of the best night views over the city you can see in Japan, and almost totally unknown to most people and the tourist book "experts".
https://www.youtube.com/watch?v=Hl1pCW9IbbkThe Kanmon tunnel is more interesting for its uniqueness than anything. See if you can get your photos taken in the middle with one foot in each prefecture.
https://www.youtube.com/watch?v=6y4K6erVyvAHagi is really a hidden gem of a place - the business hotel right next to where the bus from Akiyoshido stopped was actually very nice (it also amazingly had the fastest net speed I've ever seen in a Japanese hotel - I clocked it on speedtest.net at 60mb/s in the morning). Hagi does take a lot of time to get to, as was said, and more time to get around the city. The castle remains and park were very nice and relaxing though.
https://www.youtube.com/watch?v=wjw577xBinIThe Akiyoshido tunnel will be one of the most unforgettable experiences you ever have in Japan - but save some time to walk through the karst plateau area as well.
https://www.youtube.com/watch?v=DqIKC9S8TFQFor Shikoku, I found Tokushima City to be
the most disappointing. The view from Mt. Bizan was good, and the prefecture has some very nice areas for natural scenery, but I'd say skip the place unless you are going to see the Awa-Odori - and it looks like you will be too late for that. Takamatsu on the other hand was much more interesting. The Ritsurin Garden is just one of many nice places to see there.
https://www.youtube.com/watch?v=afx-Ju52FiYFor going back to Tokyo, instead of a cramped bus, why not take a Jet Star flight from Takamatsu? Very cheap, very fast, and you still arrive sane.