As the op did, I pull over at the first sign of pursuit, and remove my wallet along with DL, CHL and insurance and have them in hand(s) next to the window down long before they walk up.
Some ask why I have done this. I reply that I know their job and want them to feel as safe as possible. Next question is if I have a gun in the car? Answer is yes. Next question is where? Right next to my wallet.
I did pull up to an unexpected road block a few years ago. With an officer on foot in the road way ahead of me. The window was down as I noticed him in the road in advance and both hands were at 12:00 on the wheel but didn't expect that he wanted any ID. After he requested ID, I gave him both slowly and deliberately (along with insurance as they are all together). He then asked if there were any firearms in the vehicle, I confirmed that there were and he asked where. Without moving anything but a thumb and eyes I pointed up. He ducked down and noticed he was looking at the muzzle of a rifle said "Oh." and took a step towards the rear of the Jeep. Then handed everything back to me and said "have a nice day."