On that basis, methodology isn't that relevant.
I just watched a company apply SCRUM to apparently solve process problems and it just made things worse because the staff aren't disciplined or interested in what they do.
That's after five years of agile consultants and perpetual change.
If you want a manifesto with real values:
1. Fix shit when it goes wrong right away.
2. Tell people what you are doing.
3. Write everything down somewhere centrally that everyone can get to(tickets)
4. Have a rough vision and make sure people are working towards it. Don't plan the details too much.
5. Be opinionated. Someone's got to win an argument.
that's it.