It sounds like you need to get buy-in and clarify everyone's roles before you just introduce another tool into the mix.
A couple of suggestions for how to do that:
1. Show your boss what's at risk of not establishing a process. How does the lack of process affect production, goals, and ultimately revenue? Connect key metrics to the strategic initiatives they care about, and show them what they stand to lose if you don't get this sorted (and soon). This hits on a behavioral concept called Loss Aversion, and it's a proven way to get executives' attention and motivate them to want to solve the problem.
2. Get the team together for a design thinking session/workshop. Telling them a new process to follow will only get so far. Instead, get them involved in co-creating the solution so they feel more invested in the strategy. At the beginning of the session, present the challenge, the goal for the session, and then open up a brainstorming session for everyone to come up with ideas on how to solve the challenge (no wrong answers and no judgment). Give them time to write their ideas on stickies and put them up on a board. Then, have everyone take turns going up and voting on their top three ideas from the board. You can then take the top ideas and get everyone's agreement to start moving toward next steps for implementing the solution.
I'd also look into some project management frameworks for planning projects. The RACI matrix is very helpful, for example.
Hope this helps!