You could use, like sumbloke said, the NESW/Oldest tool. There you can select USA and Illinois, And then you also can select each county in IL (i don't know what happens if you select them all, but i think it would be the same as if you select none of them (like i did on the screenshot). I would assume you have to select every single county at once. (blue boxes on the screenshot)
You will get a map with the caches most north, east,south and west, and the oldest. Plus, there is a list below the map, where you can select the oldest caches. (red circle)
You could then easily add them to you virtual GPS (select the right list BEFORE you run the NESW/Oldest tool!) (orange circles)
With the number of rounds you can select, how many caches you want to see. In my selection you see the 2 oldest caches in the list. (green box)
I made a screenshot, where you can see what you can do. I hope it helps.