I find many Larsen families (northern German/Danish) but only a couple of Larson families (Scandinavian).

In the 1923 Audubon county Plat book ---
Oakfield township
John F. Larson, wife Lilly
children, Irma, Ina, Martis, Andys and Edwin F.
PO Exira R2, owners, section 5

I did find 2 wives with the name of Stena in the Audubon county Plat but their husbands names were not Lars.
I also found several Lars Larsens but none spelled Larson.

In the 1925 Carroll county Plat book ---
Newton township
Lars Larson, wife Christen
children, Anna, Mabel, Andrew, Myrna and Dorris
PO Dedham, owners, section 8 & 17

According to the Carroll county cemetery index I have there are no Larsons buried in the Carroll county cemeteries.
There is one family (Larsen)buried in the Manning cemetery.
Holger & Sophia Larsen.

I quickly looked in the Manilla & Aspinwall Centennial books but found no Larsons mentioned.
Unfortunately I don't have a Templeton centennial book.
These 3 towns are very close to Manning.

This is about all the information I have for you but I will mention your Larson family to several long time residents of Manning to see if they recognize the Larson name.