Adding "Company Name" to shipping page

I need to add “Company Name” on the shipping page /store/shopping-cart/shipping/ between Country and Address. I also would like to add a 3rd Address field. I have already figured out MarketPress Custom Shipping Form; but I want to add these fields to the top part of this page, not at the end. I can get them to show up on the page, but I can’t get them to carry over to the order page. Any help greatly appreciated!