I'm not sure how buses at NRT categorized. I think that "local" buses refers to commuter services serving towns around the airport in Chiba prefecture. I guess Nagano Snow Shuttle and JamJam might be considered "expressway" buses (kosoku bus). This may seem like extreme pedantry but it might be helpful to know that.

Given the likely need to reserve in advance, I think that the 3:30PM departure from T2 is cutting things too fine.
4:20PM departure from T3 is doable with some cushion in case of unexpected delays.

I'm not sure if JamJam pricing is dynamic? Or if you can reserve a specific seat? If so, you might prefer to reserve now.

Your best backup option, in the unlikely event that you miss the 4:20 bus would probably be to take the train to Nagano (Keisei Skyliner to Keisei Ueno, then walk to Ueno station for the Shinkansen to Nagano), spend the night in Nagano and take a bus to Hakuba the following day.

Going by train, a 5:19 PM departure from Narita T1 gets you to Nagano by 7:44 PM. The following day, you can get an 8:23 bus and be at Hakuba station at 9:25 AM. Honestly, I think that would be my prefered way of doing this trip, but I guess you might have already booked accommodation in Hakuba for the first night? Or perhaps you have a lot of luggage which makes the JamJam bus a more attractive option? The idea of being jammed in a jamjam bus for hours after a flight leaves me cold.