I have to admit that I would have little patience for such a situation, so good on you giving it a try and godspeed. I personally feel that there's a lot of interesting work out there, so I'm not sure I would even take on the project. The fact that you have a team of three people that you don't manage or have any authority over who are also majorly resistant to change their ways of doing their job in literally the worst way possible does not seem promising, no matter how you look at it.

In these types of situations, the problems are social and possibly political and rarely technical, even though the technical problems are the symptoms that present themselves so readily.