You write that ‘æggelederen og æggestokken hænger som bekendt sammen og bliver ofte omtalt sammen, og ord der ofte optræder sammen, kan smitte af på hinandens form’. I have no problem with this line of reasoning, but I would like to point out that German and Dutch do not follow suit: Eierstock/eierstok adds a syllable, whereas Eileiter/eileider doesn’t.
If pressed (by myself, if need be ;), I would hypothesise that in both languages this is because the Eierstock (ovary) contains lots of Eier (ova, egg cells), whereas the Eileiter (Fallopian tube) ushers only one Ei (egg) at the time. This logic is followed most of the time, it seems, but not quite consistently: one would expect *Eischale/eischaal instead of Eierschale/eierschaal (eggshell).
By the way, as I’m not a proficient reader of Danish, my first thought upon seeing the headline was that the ‘fuge-e’er’ was something like ‘bird eggs’, possibly an informal rendering of the actual pronunciation of ‘fugle-ægger’. Only when I came across the same word in the body of the article did I realise how far off the mark I was…