I'm going to go in order: 兄から勧められた縁談が嫌で、家を飛び出してきたというのだ。I can't believe I didn't think of the word "engagement" it sounds a lot better. I initially wanted to localize a bit and say something like "unsatisfied with the potential suitors" but I didn't want to step that far without the context.
Next: それが、家出に適当な理由かと言われると、彼は眉をひそめる。I have had 適当 in my Anki as "appropriate" for awhile now, I should have looked at the secondary definitions. The primary and secondary definitions seem like antonyms, hopefully I'll encounter this one in the wild more and the difference in usage will become more apparent. Something like "a frivolous reason" does make more sense here because my translation requires either a negative or a bunch of qualifiers ex: not a good reason or would have had a better reason. かと言われると was my first grammar hurdle. I'm still not quite sure what is going on there but I found
this DOJG entry which is how I got too "thought she would have had a better reason". I'm not sure if that's the structure that fits but it made me think along the lines of "If (it was assumed) she had a good reason, he would scowl (because she does not)".
もっとよく兄と話し合うべきだろう I seem to have really confused what was going on here, thinking that the sister and brother were discussing what she should do, instead of Ulysses thinking that she should have had a discussion before running away. It makes sense now that I have seen your translation, I probably should have started from the end and worked backwards when I was confused: Ulysses thought>(she) should have>discussed (it)>with their brother>thoroughly>before (she) ran away from home.
怒っているかと聞かれたら、怒っているとしか答えようがなかった。This one went completely downhill because I confused the recipient of 聞かれ thinking it was about the sister not asking him, rather than him being asked. I still have a lot of trouble with the れる・られる stuff, unless that's not what is going on here and I'm really lost. The tidbit about ようがない is very helpful. I find よう confusing because I originally read about it being equivalent to a simile, but that structure may just be something like のように and I have tried to fit it into everything.
嫁入り前の妹の身を案じるのは、兄ならば当たり前なのだから。I chose to omit the "younger" here because adding younger and older to siblings feels clunky in English. Ideally the reader would already know the relationships between the characters, and you would probably be using their names instead. It probably does make more sense to specify younger here cause I don't know how much a younger brother would be expected to worry about his older sister's marriage. It's nice Japanese has specific words for these relationships, since I started learning Japanese I have noticed anime where the sub/dub does not make it clear in translation but you know right away when you hear whatever word they use in the Japanese. Kind of a small gripe but it does make a difference when the siblings are around the same age or are twins or even quadruplets.