This looks almost like mission impossible in your case, cooperation is the foundation to any change.
But there is a small light at the end of this dark tunnel (hopefully not a train coming)- try to arrange demos, small presentations or even corridor chats and explain to those in charge why it is important to have proper practices.
Remember that managers usually react well to cost-benefit numbers, so try and show them that.
This is more complicated than what looks in first sight- you can start in the traditional way of showing the number of reopened bugs or bugs found in the field, talk about wasted time in context switching and lack of focus, show poor automation code since no one is responsible for it but at the end you will be asked how do you suggest to improve this and back it up with numbers.
Justifying dedicated testers as cost effective might not always be simple, personally I found myself not able to justify it even to myself and even obvious things like test automation.
TLDR; spread the word among those who have the power to decide