I think I now understand what you're asking on the "securing the carrier bracket" question. The hardware that holds the strap and spare tire up, yes?
Below is a screenshot from a 1954 Chevy Master Parts Book showing the 1950 and earlier style spare tire carrier for the 1/2 ton. It's actually a picture of a slightly earlier version that has a different "track" design and mounting than yours, but the parts that make up what holds the carrier and spare tire up are the same.
If you want to see specific part numbers, check out this
free copy of the Parts Book.
