I love it! Bartlett for America! It's a nice old fashioned biblical name which can have a few shortenings so it can sound more informal too. My son has a fairly long biblical name which gets shortened to something we call him every day, everyone says how lovely his full name is as well.
1. Yes I do think it will be shortened to Joe by most people. 2. Josiah Antonio don't go great together in my opinion because of the A sounds running into each other. I would want the second name to begin with a consonant.