What should I pay to have an 18" storm water pipe installed on my land, no obstructions, no trees, no rocks, buried an average of 3 feet deep and 320 feet long, including one drain grating?

We don't know where you are so the best approach is to get 3 competeing bids from local excavators.

In the Houston area. My engineering gave me an approximate price, our first bid was 4 times that amount. This is a one-off project, no other earth work to tie it to.

That would chap my hid too. Get 3 more bids, bids should cost you nothing but save you a ton. In the high bid, what did the bid spec for materials and how much labor?