Clan William: Mystery Muddle: The Amos Munson Family 1870 Census

CALLING ALL MUNSON FAMILY GENEALOGISTS - I NEED YOUR HELP!

Note: I absolutely don't have a solution, but the "extra" kids in the 1870 census are not the children of Amos and Mary Ann.

The story of Amos Munson and Mary Ann Kearney followed a very straight trajectory that was easily traveled both before and after 1870 until I finally located the difficult-to-find 1870 Census and then...well, perhaps someone can fill in the blanks.

Here is the 1870 Census summary where they are living in Cassville, which is about 11 miles from their 1860 location in Glen Haven:

Name: Amey Munson (Amos)
Age in 1870: 55
Birth Year: abt 1815
Birthplace: Ohio
Home in 1870: Cassville, Grant, Wisconsin
Race:
White Gender: Male
Post Office: Cassville
Household Members:
Amey Munson 55
Mary Munson 54
Josephine Munson 19
Rosalia Munson 5
Charra Munson 4 (Clara)
Joseph Munson 3
Laeza Munson 2 (Eliza)
Frank Munson 1/12

Here is the problem. When researching these children, none of them come up anywhere except in this census even using name variations. Josephine is listed as a domestic servant. I can't find who they might belong to - perhaps another older child heretofore undiscovered belonging to Amos and Mary? Yet, there is no trace of any of them after this Census. Amos & Mary are clearly living with son Charles in the 1880 census and none of these children, who would then range in age from 10-15, are with them or any of the other siblings. And, another point is that they already have a living son, Frank Munson so who would name another child Frank? The only one of these children who is plausibly Amos & Mary Ann's is Josephine, yet, she is not listed in the 1860 census with the Munson family and is old enough to have been included.

It is highly likely it is "our" Amos and Mary Ann, despite the great difference in their listed ages and their actual ages, because the next family in the census is Frank and his wife Susan and their eldest daughter, Ida.

Who do these children belong to? Did they foster orphans? I kind of like this theory - because Census enumerators often assigned the head of household's last name to all in the home, whether they shared that last name or not.

• Is Josephine, who is the only one who would fit age-wise as one of their children their daughter, or was she a relative who was brought in to care for the young brood? 
• Who did the younger children belong to? I believe they are not Munson at all and even if Munsons, not Amos & Mary Ann's.

Theories? Facts I've not yet discovered?