Gotta be honest, Ryou is rushing this. Mao returning the call through Esemori's phone and Yumiko's death are literal conveniences to wrap up ASAP. But somehow both make sense, storywise. It's only the execution that exposes the speedrun.
Something you have to notice... with Yuri imposing herself as a partner in crime and use Nagi's phone to keep in touch with him without asking Reiji first if he was okay with that, she shot herself in both feet. She still is treating him like a child to her own convenience, however, she doesn't know Reiji has a talent to backstab and betray people (as shown when he baited his mom into doing double suicide and then pull a solo suicide in front of her very eyes) when they stop being useful or are getting in his way. In that sense, he is the spitting image of his mom: she used Uryu to her own convenience, and when she realized at the last minute he was getting in her way to Akira, she stained her hands by killing him. Reiji may have found a way to kill 2 birds with just a stone and not have to stain his own hands unlike his mom.
Considering there were quite several coincidences, maybe Reiji doesn't have to go to Tokyo, because Mao has to go to the town to do some recognition of Esemori's estate for the inheritance and funeral paperworks and arrangements. In that case, Reiji can tell him where Nagi exactly is and then set the trap for both Mao and Yuri. The teacher kills the uncle, but Reiji, with the evidence of Yuri having Nagi's phone and the incoming and outcoming calls record, can sell Ishibashi a convincing story about having a hint about Nagi's whereabouts, and told her only alive relative about that to go and rescue Nagi, but he also "disappeared after reaching the exact location" for the only sake of throwing Yuri under the bus.
The question here is who will betray who first: will Reiji get his way first, or will Yuri's jealousy make her kill Nagi??