Alternatively, you could forgo the JR pass and fly instead.

You can take a flight from Itami to Hanamaki. From Hanamaki airport, you can take a bus to Morioka and then train to Tazawako. (Taxi to Shin Hanamaki, then trains also works). This lets you sidestep the challenge of getting a seat on trains in and out of Tokyo at a busy period.

I haven't done the sums, but if you get a cheap seat on a flight to Hanamaki and then take trains to NRT at the end of your stay, I don't think you'll spend much more than if you purchased a JR pass.

(From your dates, I'm not sure if a 7-day JR pass will span all the travel you're hoping it will cover).