I think your key question is to find a path for this project. Probably best to get some "outside" advice on setting this route, but not a high priced consultant.
You probably have another department in your company struggling with the same objective. Say "Accounting" is going through the same process, try teaming up with your counter part in Accounting and maybe a Lean mentor for a department who has implemented Lean. The three of you should sit down and do the first step - map your "Value Streams". This will drive you to understand why you are doing things the way you are.
Everyone wants to "do it right the first time", but once you understand your deliverables and measurables you can see where the waste it. You will be surprised what some one who understands "what" you do, will question "why" are you doing this?
If there is a mistake made in Engineering, what is the cost? Huge cost and deliver delays? Outside warranty cost? Minor shop rework/repairs? Should you be checking your drawings more thoroughly? less checking? How much time should Engineering staff spend on the shop floor?
What about drawings and documentation? Are your downstream customers using these? What level of detail should be shown on assembly drawings and BOMs (fasteners? etc.)?
I encourage you to think fundamentally about how you spend your resources. Lean implementation is not meant to be a something where you just shuffle the seating plan.
Best of luck,
ERT