These are my favourites for you:
Eric - I love how simple and recognisable this it. It's great with Troy and Rex. It's a name of kings which fits in with the theme.
Victor - this is amazing. I really like it with the bros, it fits right in.
Conrad - I like it with T & R, it's got the same great man with armour feeling. They're all spread out; Troy (Anatolia/Turkey), Rex (Rome/Italy), Conrad (Gaul/Germany).
Ajax - I've always liked this name, and it would be cool if someone used it. I couldn't, I find his insanity and suicide a little troubling, and there's a famus Dutch football team by this name.
Milo - I feel this is very soft next to Rex and Troy. Milo is a poetry writing little lad. But I do love the name, very beautiful.
Paris - how I'd love for someone to reclaim this name... although I never liked Paris in the stories, the name is lovely. Did you ever consider big brother, the gorgeous mighty warrior Hector?
Hector is a great suggestion!
Eric! And Conrad! I either one could be a nice fit. Victor will probably be on the table until the last moment. It's a family name and it fits with Rex and Troy. I don't think I can actually use Ajax, but it just keeps calling out to me. I love Milo. It's such a great name. Too soft though for my wild and crazy Rex and Troy. I mean that too. My boys are wild and crazy! It would be nice if the boys took Paris back, wouldn't it? And yes, we've thought about Hector. But our last name is He****. I just can't pull off Hector He****.
Where did you find the meanings you listed?
Some of them sound a little weird to me.
For example Adler is the German word for eagle, it's just the translation (by the way, it's not a first name in Germany, it's a surname though, often Jewish). I don't know where "Resembling a soaring eagle" should come from.
Same with "Braun", another German word and surname, German word for "Brown". It's just a color, i don't know why it should mean strong or anything related.