You would do well to take a look at memoirs by various polar expedition leaders (or possibly other members), or books about them... particularly Knud Rasmussen specifically, or other Scandinavians like Roald Amundsen.

By way of example, one I've read a few books on/by is Fridtjof Nansen; he was a few decades earlier than your man, but very influential, and his memoirs are packed with details such as supply lists. The most detailed in this respect was his first, The First Crossing of Greenland. This was a 6-man expedition in 1888, crossing Greenland on foot. There is also some great info in his second, Farthest North (vol 1, vol 2) about the 1893–96 Fram expedition; of particular interest to you is the logistics planning for the break-off expedition by he and Hjalmar Johansen: the two of them (plus dogs) went it alone on the polar icecap for more than a year. Their experiences could also be of interest for your 'exploring on their own' angle. Anyway, as I say, this is a little earlier than Freuchen, but may be useful to augment whatever other info you find.

e: words