Wow. I've never thought of this... I can think of three places I've reached out to in order to have a company manually update my address because of this just in the last two months.
I always tried it first, and if needed would reach out to the company afterwards.
Had one company call me after tweaking the form in Chrome and ask how I managed to place the order with that address. After playing dumb for a bit, I sheepishly admitted to altering the form. They were upset at first, but after explaining that they used USPS and USPS handled mail to PR just fine and required no export papers, they actually thanked me and updated their site themselves to handle shipping to PR.