good grays are hard to get, period.
there are other factors too, and some of them may be making your challenge worse, or they may not be... but in my opinion, the grays are going to be hard to get anyway.
My experience was that saving my grays (actually 99% of all my prints) as rastor images, in RGB mode, gives me better grays.
I have also found my laminates to add a greenish tint, and agree that the appearance of prints inside the shop can be dramatically different than in the sun. In the case of greenish tints on blacks or grays, my fluorescent lighting hides the problem from me, & than the sun makes the problem 10 times worse.
Before I figured out to check my grays in the sun, I got my neighbor's test prints (& colors) approved and printed two 54' logos for his Sprinter on 3M180c, I laminated them & scheduled the install... then the day he dropped off the van, we walked out in the sun & his Grey AND yellow had so much greenish tint I knew I was in trouble. We cancelled the install, showed the client & ordered some 2 mil gray & yellow Arlon. I cut the shapes I needed, & applied them to the 180C. so I would still have some of the 3M characteristics of the 180C, plus it helped me position all the parts on the greenish prints & then have just one piece to install on each side. (fortunately we hadn't approved the lettering layout yet, so nothing else had been printed besides too logos)