I never understood why they had deadlines...
It gets done when it gets done, but it gets done right.
Sure, there's things like show dates to meet and stuff like that, but cripes, they should know by now how long it takes to do what they need to do to build a car.
Schedule properly for it and add in some buffer for screwups.
I'm pretty sure they can find work to fill in the time should they actually finish ahead of schedule. Like, get a head start on the next project or help out on another that's falling behind. If not, they can always go out on one of their idiotic field trips instead of going the day before one of their deadlines when there's "3 days worth of work left and only half a day to do it."
If someone brings them a project with an unrealistic schedule, say, "No."
If you say, "Yes", then hire on some extra help on a contract basis and keep everything else on track. If you're doing double the work, you're making double the money, so why not double - or almost double the workforce?
Of course, you could probably get away with much less than double the workforce, but you see my point, right?
You'd then have the opportunity to hire experts based on the requirements of the project.
If you use this as part of your marketing and sales strategy, the high-dollar customers are not going to mind. In fact if you do it right, you can charge more.