Problem if visa/green card name spelling won't match existing US records?

[DKNC 21]

My spouse has an IR-1 visa interview coming up soon. The embassy insists that the name used for the visa must match the machine readable line in the passport. This will be the second time my spouse applies for US permanent residence. The first time was before machine readable passports, so the Scandinavian vowel ø in the last name was simply replaced by an o. There are now over 20 years of records in the US under the Americanized name. The Swedish embassy insists that regulations state that the vowel must be spelled out as oe to match the machine readable line on the passport and to do otherwise would cause problems with entry into the US.

Documentation was sent to the NVC indicating why it was important to spell my spouse's last name the American way. The information on the CEAC site was upated, so we thought all would be fine. When the embassy sent an interview confirmation email, we noted the extra e in the name. The email responses have been insistent that the only way to drop the e would be to have the Danish passport changed. Doesn't seem like a real option as my spouse is not going to make a legal name change.

My questions to those that have gone before us:

1. Will a name spelling difference between the visa/future green card and the existing social security card cause any problems?

2. If by some miracle we can convince the embassy to use the Americanized name on the visa, will we have trouble with CBP every time we travel?

If anyone else has dealt with various name spellings on US documents, I would love to hear about your experience.