Emigration honestly is the most logical option for a felon. A few nations will accept local background checks in the immigration process, so if you move to a state where you don't have a record you can just get your police report from a place where your record is clean.
Another option is to go live in a Compact of Free Association nations such as Micronesia or Marshall Islands. US citizens are authorized to live and work there without a visa, so once you live overseas there for a few years you can immigrate to most other nations using the background check from your country of prior residence, which is now a country where you have a clear background.
Another option is to go live in a Compact of Free Association nations such as Micronesia or Marshall Islands. US citizens are authorized to live and work there without a visa, so once you live overseas there for a few years you can immigrate to most other nations using the background check from your country of prior residence, which is now a country where you have a clear background.