How does a stateless person (one who voluntarily renounced their citizenship while in country) provide identification, arrange travel visas, and get back into the US?
Short answer: You find a country who is willing to recognize you as stateless, and issue you travel papers. At that point you can enter the U.S. by applying for a visa.
The USA really does not want to create stateless people. They are laboring diplomatically to eradicate statelessness. As such, the State Department will want to see that you are secure in another country's citizenship before they will repudiate your US citizenship. Otherwise, they are very reluctant. The State Department will insist you do the repudiation in a foreign country at a US embassy. If you want to become stateless with your feet in the United States, you'll likely have a legal fight on your hands.
Regardless, it will cost you $2300 in filing fees (plus, all your back taxes) :)
At that point, you become the problem of the foreign country. You aren't anyone to the USA, and you have to apply for a visa just like anyone else.
When a stated person enters the US, immigration's pivotal concern is whether you'll leave the US consistent with the terms of your visa, i.e. return to your country of citizenship. Being stateless increases this risk, and being a USA expat increases that risk further, since you are so familiar and comfortable in the US.
If you found yourself in the kind of piccadillo that would qualify a foreigner for refugee or asylum status, the US would consider it just the same as others, since those statuses include right of residency. Some countries manufacture stateless people, e.g. Syria will not grant citizenship to a non-Muslim born there.
It does not appear there are any provisions for stateless people to enter the US or identify themselves therein. The US didn't ratify the UN Convention relating to the Status of Stateless Persons. If you manage to get into the US you will not be able to open a bank account or do anything else that requires ID.