New York, outside of the NYC area, is not as bad about FOPA as people think.
That said, you should go above and beyond. Ammo and guns in separate containers, all locked. Heck, buy a third lockbox, and put the keys for the other containers inside that, if you want. it's not legally required, but having to unlock a box to get the keys to unlock the other boxes can't hurt when it comes to either roadside perceptions or (if the worst happens), in front of a judge. Make it a series of Russian nesting dolls safes if you like.
I don't know about "all the northern states" not honoring an Iowa permit. The three most northeastern states (VT, NH, ME) are all constitutional carry and don't care about permits.
I've driven the length of NY multiple times with guns. I didn't sweat it. I even had a nice conversation with a NY state trooper along I-90 outside of Syracuse, while I was waiting for a tow after our trailer burned a wheel bearing. In a Texas truck towing a trailer with Texas plates... he didn't even ask. It would have been an awkward conversation, because inside the trailer I had dozens of firearms and hundreds of pounds of ammo. I was covered by LEOSA at the time, and was carrying two handguns; NY was less accepting of LEOSA than they were of FOPA in 2012, but even though there were horror stories about NY, the topic of guns never came up.