The Oklahoma Tax Commission has assured the Oklahoma Society of CPAs that any paper returns filed will be processed, e-filing mandate notwithstanding. I put a sheet of colored paper on the front that explains why the return isn't eligible for e-file.

That said, entities don't really piggyback. I think if you uncheck to e-file Federal and check to e-file Oklahoma, then go through the normal e-file process, that the return will file without issue.