> Eigi urðu allir svo haldinorðir að þegðu yfir ódáðum þeirra eða
illsku að eigi kæmi upp um síðir.
> Not all were so discreet (Z) that they were silent over these
mis-deeds and wickedness (stuck here) - the story got out

Fairly literally: "They weren't all so discreet that they kept quiet
about their misdeeds and wickedness so that it didn't come to light in
the end."

It might make it clearer to translate the two subjunctive clauses ("so
they they kept quiet" and "so that it didn't come to light") with
English infinitives: "They weren't all discreet enough to keep quiet
about their misdeeds and wickedness and thereby stop their crimes from
coming to light in the end."

'þegðu' = ON 'þegði', 3rd pl. subj. of 'þegja'.
'kæmi' = early ON 'koemi', 3rd sg. subj. of 'koma'.
'koma upp' "come to light"
'um síðir' "eventually, in the end"

I notice the version you were working from had a typo, 'aeigi' in
place of 'að eigi', which can't have helped... But all those negatives
can be confusing too! If worst comes to worst, we could always resort
to logic:

1. If they aren't discreet, they don't keep quiet.
2. If they don't keep quiet, their crime will come to light.
3. They aren't discreet.

THEREFORE, by hypothetical syllogism, their crime will come to light!!

> Nú bjuggu þeir skipið snemma um vorið, það er þeir bræður höfðu átt,
með þeim öllum gæðum er þau máttu til fá og skipið bar,
> Now they made ready their ship early in the Spring - that same which
the brothers had owned, with all the goods they could take to the ship
(implies all the ship could carry)

> that same which

That's right: 'skipið [...] það er' "the ship which".

> with all the goods they could take to the ship (implies all the ship
could carry)

"with all the goods they could lay their hands on, and which the ship
bore" (i.e. could carry). Notice that 'bar' is singular, agreeing with
the ship, rather than them.