The OP did not mention moving in with the brother. She wrote:
"Would my name showing up on an apartment lease be enough to prove U.S. residence? My brother lives in the U.S. and he can likely get me into his current lease."
To me, this sounds manufactured, like a paperwork modification vs an authentic piece of evidence of domicile. Maybe to you it is not a big deal, but per the TOS rules here at VJ, we cannot recommend creating evidence which is not in good faith. The best evidence for all steps of US immigration is genuine evidence. Yes, even for low-fraud, low-risk consulates.