Hakkoda - is that a stop on the JR Bus that goes from Aomori to Towadako, the ropeway stop? You could consider taking that bus all the way to the lake or to oirase stream. I don't know the onsen spots you mentioned

The Resort Shirakami was nice. You see some nice coastline - and lot of water (nice being faint praise). I think I might have preferred to just take the regular limited express that goes over the mountains, via Odate IIRC. It follows the coast for a bit north of Akita. I think you need to be a train fan or love views of ocean (Nihon Kai) to get more out of the trip than I did (i went in the opposite direction).

If you are just going to Akita to spend the night before going to Kakunodate then I suggest just taking the shinkansen from Aomori to Kakunodate change at Morioka. Even if you were planning on seeing sometshing in Akita-shi, I suggest that you don't really need to do that and just spending the night is fine if you really want to take that scenic train. Kakunodate is special. Stay at the Folkloro hotel next to Kakunodate Station, if you can.

One shinkansen stop east of Kakunodate is Tazawako. You can visit the lake or not. The real attraction, imo, is Nyuto Onsen which is among the best onsen spots in Japan. Better to spend the night there but it can be a day trip.

Lodging in Kakunodate and Nyuto Onsenkyo might already be sold out, so you might need to spend the night in Akita or Morioka.

To sum it up, your plan is spend a day on Resort Shirakami and night in Akita. My suggestion is shinkansen to Kakunodate to spend the day at Kakunodate and night in Akita, Kakunodate, or Nyuto Onsen. That would be the 25th.

You could skip that night in Sendai. Add that night to northern Tohoku. On the day you travel from there, if the weather is nice you just get off at Sendai to go see Matsushima. If the weather is not nice then you can still visit Matsushima - am assuming the boats to out in the rain because Japan.