I have heard from more than one source that SAS is the airline to go with for Americans to visit Sweden. My American fiancé was not allowed to board the flight to Sweden from the States with Delta, because he was not a EU sitizen. Every airline got their own set of rules, even if you would be an exception from the travel bans, the airlines do not want to risk you not getting in and just says no before the travel begin - which they could do when you buy the ticket, but why do that when they can make money off you and let you pay and then stop you at boarding. Some new type of scam right there.
K1-visas are not an exception from the travel ban in The States, and K1-visas are not getting processed at the moment. Only spouses are. Me and my fiancé were recommended by the American Embassy in Sweden to not do the K1 and get married on paper and apply to the spouse visa instead. BUT, it can take months to get approved and for me to travel to see my then husband in The States on my ESTA while my I-130 form is pending, is risky since it is up to the custom to let me in based on the proof of our marriage.
All of this is insane according to me, splitting apart families and partners. It all just says "the wrong people in power" all over it. Might turn out to be a great story to entertain future children, but today it is just messed up and torture being away from each other.
I appreciate this discussion forum and hopefully someone will write good news soon.