This was originally a comment, but it seems to be what OP wants, so I'm reposting it as an answer
I would use ctrl+z to suspend your live, running process. This will leave you with a PID, which you can later resume with a call to fg
: fg <job-number>
.
This shouldn't have any implications with changed network settings (like IP, etc), at least as far as python is concerned. I can't speak to whether the API will freak out, though