Norwegian Air booking USA vs other countries

This isn't directly an answer to your question, but, as a frequent Norwegian Air Shuttle customer, I find Norwegian's pricing a frequent mystery. I just now plugged in the dates of your travel from LAX (Los Angeles) to Rome. I realize you are not flying from the west coast, but.....the RT fare for their "Low Fare+" was less than $900 and that's a journey approximately 5000 miles farther. I presume they (Norwegian) are trying to establish a strong following out here in the west - I'm flying to Paris the same day as your trip to Rome.....my flight is Oakland to CDG and it is less than $300 (one way) for their "Low fare+". I know this hasn't been helpful - but I hope it sheds a little light on Norwegian's business model.

Because you're not a Norwegian national (but you're acting like one by trying to book through their site). This would apply to any international airline site that has a US version and a national version. As for the prior comment, airline fares are not priced solely based on distance - that's only one variable of many that drive the dynamic pricing algorithms. Also, they can sell an x number of seats as loss leaders as long as the others are priced in a way that meets their revenue targets. People tend to think that budget airlines price all their seats at ridiculous low prices but that can't be the case; they still have to cover their costs plus some profit margin. Same way that Bolt or Megabus markets their service as "low cost tickets from $1". Only a small percentage of those passengers literally pay $1.

Read the part about "resident fares" in this NYT article: https://www.nytimes.com/2019/03/29/travel/airline-booking-strategies.html
"Sometimes a ticket purchased from within a foreign country costs less than the same airfare in the United States. That’s because airlines price their flights based on competitive factors in local markets, including the wealth of consumers and their willingness to fly.

Airline search engines can tell where you reside based on your computer’s internet Protocol or I.P. address. Users can mask that address by subscribing to a VPN or Virtual Private Network, which allows you to search anonymously (plans at NordVPN, one provider, start at $2.99 a month). Some travel strategists believe this works."

Someone else posted here that they were able to book on Norwegian.no successfully. I can't find the post now - sorry.

We recently flew Norwegian to return from Italy to the U.S. We booked on the Norwegian /.no website, for savings on a similar scale to the OPs. There were no problems.
The confirmation email one receives in in Norwegian, which is daunting at first, but the six-digit confirmation code one receives works on the U.S. website, in English, so there were no problems with doing any of the necessary follow-ups.

Thanks all for taking the time to respond.
Saskal, your response was most helpful.