Even thinking this is an option suggests to me a lack of realistic expectations.
Interesting analysis. Perhaps it's my mushy thinking, but I'm unclear as to your solution regarding the problem at hand.
The way the "problem" has been framed there is no viable solution. There is just no way anyone can walk 400 miles carrying a child and a small dog and a heavy pack containing everything all three of them will need.
Regardless of an individual's fitness level, experience, and/or equipment, there is no way that the task being described can be accomplished. Just cannot happen. No amount of gear or advice can make it do-able either.
That suggests to me that it is time to re-evaluate the supposed problem.
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Warning - I am not an expert on anything having to do with this forum, but that won't stop me from saying what I think.

Bob