14-16 Day Trip to Norway next July/Aug as Honeymoon - 4k Budget per person?

Yes, it can work.

Consider also Bergen not only Oslo as international airport (Europe).

As soon as you have an itinerary try to do early booking / reservations. For booking hotel chains use their member programs.

If you will have a rental car for western fjords you can save parts of NiN.

Fuel and food are cheapest in towns with ports or at large street axises such as E6.

Consider Hurtigruten or Havila port-to-port offerings to get from Bergen to Alesund or even up to Lofoten.

Just as info: This article from this year shows the price index levels of European countries compared to Germany. Norway was once leading the table but their currency gets weaker.

We went last September for 18 days at a total cost of $8600. That included everything (including airfare, trip insurance, extra car insurance, and airport parking). We've done six trips to Europe, and Norway was our least expensive one.

We booked a lot of cabins so we could prepare our own meals.

I think dropping a car at a different location and going up to Lofoten will increase your costs over what you want to spend.

If you decide on Norway, book your accommodations ASAP.

Best Wishes on your upcoming wedding!

I will add that you should not feel constrained to fly into Norway from the US. You might find it's less expensive to fly into another city and take a cheap internal flight, train, ferry, whatever. Sure, it takes some of your time, but maybe you'll decide that a couple nights in Reykjavik or Dublin will add to your experience.
I'm not sure you need a car for this agenda. Take a look at the trains and ferries to see how much of it you can do (and for how much) without the car. Here is some information from The Man in Seat 61: https://www.seat61.com/international-trains/trains-from-Oslo.htm
Another way to save would be to stay in more modest accommodation and just book a couple of nights in an upscale hotel/resort or a unique stay like one of these: https://www.visitnorway.com/hotels-more/unique-accommodation-options/

Congratulations on your marriage, and enjoy your trip and the planning of it!

Congratulations! Norway is a wonderful spot to explore especially if you enjoy hiking. One planning idea to keep in mind is that Norwegian hotels, even the less expensive ones, have some of the best breakfasts anywhere so you can definitely feed yourself to last a good stretch of time. The breakfasts are usually part of the hotel rate so it’s one way to save some food money.

Just wanted to come back here and thank you all for your information. Has helped me begin to plan this!

My beloved spouse and I spent a little more than you have budgeted over a similar time period this past September. We might have been able to save a little if money was tight. You’re not far wrong. Best wishes.

Congratulations! We Just visited Oslo, Bergen, Alesund and the western Fjords last year. You will save a boatload of money if you stay in vacation cabins with kitchens when you’re on the road with a rental car. There are tons of cabins available in Norway as Norwegians have vacation cabins they often rent out when not in use. RESERVE ASAP for summer because the best properties get rented out early as most travelers visit Norway during summer and tourism is exploding there. Try to rent a Hybrid vehicle because gas was $9.50 per gallon so an EV or Hybrid saves a lot of money. www.AutoEurope.com has good deals on vehicle rentals with most rentals available at airports. They do have expensive one-way dropoff charges ($500-$1,000) so plan to return the car where you picked it up. We found renting a car for 24 hours to drive from Bergen to Alesund would cost $600 with the one-way dropoff charge. We opted to fly on Wideroe Airlines for $200.
In Oslo, Bergen and Alesund. we rented apartments with kitchens through Booking.com. and this saved another boatload of money as restaurants in Norway are ridiculously expensive and serve mostly mediocre cuisine. I can PM you the properties we stayed at in Bergen and Alesund if you’re interested
If you have enough room in your luggage, pack a collapsible cooler so you can picnic and transport groceries. Otherwise, buy an ice chest at a grocery store.
Have a great honeymoon in beautiful Norway!