Justin, We had the source for Odinkar in A.Bremen's brief note regarding the bishops father and relation to the danish kings, his father was Toke jarl, and no one have ever to my knowledge questioned that, accept Anette who demonstrably cut off his father and locked the profile with a note that his parents was unknown.
The controversial part here, was that he was set up as the son of Gorm. I'm not the only one who have came to this conclusion, that Toke jarl Gormsen actually was that father, because we thereby gets directly connected with the royal family in Denmark,
which in turned was a part of that short notification A. Bremen made.
When going thru alternative candidates named Toke both contemporary and related to the royals in Denmark, we end up shorthanded with no other better candidate and we do not need to really question this as there aren't any other to choose.
If we accept that this far back in time, we will likely never find any much written birth certificates, or documents without contradictions, we would understand that we can't always have the same high demand on verified proofs as we have today straight transmitted into this early medieval time. This mean in clear, that if we want to have certain profiles in the tree, we will have to settle for less, not meaning that anything goes, it still have to be realistic, chronological and make sense based on the little info we use.
This mean that you're wrong in your attitude Justin, because most of the profiles in the Scandinavian lines this far back are often based on short text notes, sometimes only one row, or just a name. Nothing is 100% bulletproof, but A. Bremen was almost contemporary with Odinkar, unlike Saxe Grammaticus who likely was born almost 200 years after the death of Gorm, menaing, there would be a higher probability that the sources Bremen used are more valid, than the sources Saxo used, the more contemporary some historian or writer was with the subject, the more credibility we can put in their works. (As a fun note, Bremen called Gorm "Wurm")...
The next thing we use is a compilation of texts in order to see what they agree or disagree on, here we can use a lots of sources, including maps and also combine this with e.g. archaeological findings, or why not, DNA. Together it creates a broader picture of the described events, some parts in some sources can be ruled out because it doesn't fit chronologically, or we already know a more truer ground, as an example we can take Jomsborg, according to the Knytlingasaga and Fagrskinna, Jomsborg was built by the Danish king Harold Bluetooth in the 960s. The Jomsvikinga Saga mentions Danish Viking Palnatoki as its founder. Here we have two different theories, a third also did exist, it was only just a legend!
But we know by archaeological findings that they actually built places like this and in autumn 2014, "a golden disc bearing the name of Harald Bluetooth and Jomsborg appeared in Sweden. The disc, also called the Curmsun Disc, is made of high gold content and has a weight of 25,23 gram. On the obverse there is a Latin inscription and on the reverse there is a Latin cross with four dots surrounded by an octagonal ridge. The inscription reads: "+ARALD CVRMSVN+REX AD TANER+SCON+JVMN+CIV ALDIN+" and translates as "Harald Gormsson king of Danes, Scania, Jomsborg, town Aldinburg"."
https://en.wikipedia.org/wiki/Jomsborg
Until the finding of that disc, it could have just been a legend. If Harald founded Jomsborg, it would also make sense that his brother became jarl there, and yes, this is right in the Vendland, and still, dux Winlandensis fits right in so when you claimed, that you would "leave open the possibility Adam of Bremen is speaking anachronistically. He might not be completely reliable on this detail.", regarding the place, you actually just guess that he might be wrong about where it was, I say this, Adam of Bremen was right, you and Anette are wrong, and with this place, we also strengthen the possibility that he also was Haralds brother, NB, I say possibility, not 100% proven fact. I could be wrong, but I don't think so, remember, I'm always right to 99.9% in whatever line I previous connect and or merged up to now.