Why don't you use a 3/8" NPT to 5/16" hose barb? The short piece of hose that comes on a stock injector will fit a 5/16" hose barb.
Googled and found this for example but you can get them at any hardware store - http://www.boydwelding.com/products/parts/brass-38-npt-to-516-hose-barb/
Googled and found this for example but you can get them at any hardware store - http://www.boydwelding.com/products/parts/brass-38-npt-to-516-hose-barb/