Most of my family is from Tromsø. Hands down the most beautiful place I've ever been. Though Slovær, Bodø, and Harstad are also rife with staggering beuaty. I miss it so very much. Can't wait to go back. Maybe next time I'll stick around for 2 years and get some family sponsorship for my dual citizenship! ;)
From January 1 2020, dual citizenship is allowed :-) https://www.udi.no/en/word-definitions/dual-citizenship/
There's also one more loophole already existing -- if you acquire Norwegian citizenship, and you cannot afford to renounce US citizenship (now that they have upped the price of renunciation so high). You do have to prove it with the right income amount or lack, etc. Best of luck!
+1 Especially the fishing there is just awesome! I could literally spend my summers there on a zero budget. Just eat fish, crustaceans and some healthy algae. All there for the picking when the tide is down. Well, the fish will usually cooperate if you just cast something in the water reminiscent of a lure.