In such a short distance between Omagari and Morioka, there is no huge difference in the times needed between Shinkansen and local trains. Also, there is no limit on the number of tickets for local trains. Or, JR just determines the number of special services based on past situations. You don't have to worry about that.
This is a list of the special services on that day for three directions, to Akita, Innai, and Morioka. The capacity seems like the most in the Innai direction. The least in Morioka, the farthest.https://www.jreast.co.jp/akita/press/pdf/20180710.pdf
This is the resulting timetable on that day, also with regular services. There are 22 trains from Tazawako to Omagari with the arrival time from 11:14 to 19:16. Of which 18 from Morioka, Of which 13 are Shinkansen and the remaining 5 are local trains. There are 13 return trains from Omagari to Tazawako with the departing time from 20:48 to 24:39. Of which 11 to Morioka. Of which 6 are Shinkansen and the remaining 5 are local trains.https://www.oomagari-hanabi.com/images/timetable92_2.pdf
Katakai states 4-shaku while Nagaoka 3-shaku for the maximum size of firework balls. But the masses of gunpowder are the same.
Here is another comparison between Omagari and Nagaoka. The number of visitors and fireworks. Omagari is held in only a day, more intense than Nagaoka.
Omagari: 0.74 million / 1 day, 18000 / 1 day
Nagaoka: 1.03 million / 2 days, 20000 / 2 day
I have checked the accommodation availability on that day with Google Maps. There is a huge hole centered at Omagari. JR allows the following destinations on that day.
Omagari 21:53-(Akita)-(Oiwake)-23:39 Oga
Omagari 23:21-(Yokote)-25:43 Ichinoseki
Omagari 24:31-(Yokote)-(Innai)-26:16 Shinjo
Omagari 24:31-(Yokote)-26:12 Kitakami
Omagari 24:37-(Akita)-(Oiwake)-(Hachirogata)-(Higashi-Noshiro)-27:04 Odata
Omagari 24:39-26:06 Morioka
Omagari 25:11-25:43 Akita
Morioka still has hotels available. You just need to get to Morioka. There is an overnight bus from Tokyo to Morioka, but I would try a non-reserved seat on Tohoku Shinkansen Yamabiko (Hayabusa, Komachi, and Hayate are reserved seats only).
But, according to JR cyberstation, I found many Tohoku Shinkansen still have seats on the 25th. Only two has no seats, Komachi #1 and Komachi #7. There are so many Shinkansens. If you want, just reserve one.http://www.jr.cyberstation.ne.jp/vacancy/Vacancy.htmlhttp://www.eki-net.com/pc/jreast-shinkansen-reservation/english/wb/com...
OK, ok. I have confirmed Komachi Shinkansen trains between Morioka and Omagari are booked out. But there are local trains. So you could reserve a Shinkansen to Morioka, check-in there, get on a local train to Omagari, enjoy the fireworks at the Sajiki-seki, and get back to the hotel at Morioka by a local train. That would be a way to go.