Can I span 23 feet with doubled 2x8 floor joists?
No, you cannot span 23 feet with conventional lumber, even doubled. It'll be as bouncy as a trampoline and won't meet code, and that's if you can find such lengths. 

You'll need at least a 12" (nominal) I-joist or an engineered floor truss to span that far, or you'll need an LVL or steel beam midway. 

None of us can offer more specific advice without a site visit, and most of us aren't engineers anyway. There's really no way around having a qualified local expert stop by.