I've got the book also and I think it was just a typo about the Springfield being in .303. Also, the "Mauser action" description probably meant a "bolt action". Just my best guess.

"Osa pictured in the Serengeti with her new Springfield rifle, 1928."
From: http://www.safarimuseum.com/museum_shop/postcards/postcards.htm

That's definitely a Springfield action. I believe it was a sporter in .30-06 by Griffin & Howe.

Osa Johnson with Winchester Model 1895 rifle in .405 Winchester.
(The description and list of their rifles is given in "I Married Adventure".)

Black Rhino / Thomas Bland double rifle in .470 Nitro Express.

http://www.safarimuseum.com/

Also, see this thread here on nitroexpress: Osa & Martin Johnson - Photo Archive

-Bob F.