Unless you have thousands to spend on custom profiles just to make it better, learn to design away from large areas of grey in the future. There are so many variables, RIP, Ink, Linearization and profiles, material, laminate, and lighting conditions (sunny, cloudy, morning, evening, inside, and out). Greys were so frustrating that in the past I resorted to using halftone dot patterns to create greys on a few projects. I don't have a printer at this time but I have heard that the HP latex and Rolands with light grey do a lot better job of printing greys and halftones.
This is an age old problem and your not alone. I have been here since 2008 and greys are a problem for most, and grey gradients are a nightmare. If color is critical make sure you print a proof on the actual material, laminate it, and have the customer view it in the conditions it will be viewed in - vehicle wrap, exterior sign; outside in the sun, interior sign; inside under florescent lighting.
Laminating your proof is important because of the varying amounts of UV inhibitors in different laminates will make a difference in the color shift.