Lots of suggestion that will work but I've not read (have not read ALL the posts) the way I'd go at it. First acquire a surveyors transit. (Since this is a one time project, I'd think about just renting the transit.) A model where the optics can be flipped end for end. Set you end stakes, place the transit near the high mid-point. Sight in one end stake, then flip, not rotated, and see how close the other end stake is lined up. Reposition the transit as needed until both end stakes are lined up by just the flipping the optics. Now you're ready to place all the other posts by sighting them through the transit.
Here's apic of the type of transit I'm thinking about.
Vintage Used Old CL Berger Sons Boston Mass Surveyors Transit Tool in Box | eBay