I just started doing package deliveries, and I have the exact same issue... It's very frustrating because as you say, it recalculates the route looking for sidewalks/walkways which not only takes several seconds, but the new route can lead to an undrivable path (which could be dangerous if you aren't familiar with the area).
Unfortunately I don't think there's a way to keep it from switching automatically when the distance is so close... I don't see any settings for it. I might have to find another app that keeps one mode only. I don't know if Waze does, but I might try it.
Another option that could work, but I haven't tried it yet would be to have one route with a bunch of added stops, which I think would keep it in driving mode, but that would be a pain to set up for so many stops...
Hopefully someone else can chime in with some better suggestions!