We plan to walk from Magome to Tsumago on April 1st and afterwards we need to get to Takayama.
Is the fastest way to do that is to walk to Nagiso and then take trains to tsumago? Hyperdia suggested a few routes but they really varied in length and seemed to only work until early in the afternoon.
To make your way to Takayama from Magome/Tsumago, your best bet is taking the Shinano Wide View express train from Nakatsugawa to Matsumoto and then taking a bus to Takayama.
The Shinano Wide View passes through Nakatsugawa about once every hour and takes about 75 minutes to reach Matsumoto. It only stops at Nagiso a few times during the day: 8:00, 11:00, 16:00, and 20:43. I recommend starting your walk from Tsumago instead of Magome so that you can reach Nakatsugawa Station more easily.
Since the last bus that leaves from Matsumoto to Takayama is at 17:05, the latest trains you could take would be: the 14:49 Shinano Wide View from Nakatsugawa (arrives at 16:04) or the 14:44 local train from Nagiso (arrives at 16:41).
I hope that helps answer your question.