Not that I actually know much about Homeric Greek, but the infinitive does work better than the imperative, because it makes it less personal and more gnomic: it is a statement to the world, not a command to the individual. Although in context, it is not a command anyway, but reported speech:
“Hippolochus begat me. I claim to be his son, and he sent me to Troy with strict instructions: Ever to excel, to do better than others, and to bring glory to your forebears, who indeed were very great … This is my ancestry; this is the blood I am proud to inherit.”
So grabbing Homer’s “ever to excel”, and changing “excel” to “ascend” in the infinitive, would be a good thing. Although I’d go with an antick Homeric infinitive, so αἰὲν ἀναβαίμεναι, rather than ἀναβαίνειν.
But you want to be careful that “ascend” in Greek has the same connotations as “excelsior”. Looking at LSJ, I’m seeing ἀναβαίνω have meanings like “go up to heaven”, “trample on the dead”, and “go on board a ship”; we can pass by “go on a podium to make a speech” as Attic, and “get on top of” for sexual purposes as… well, you know, I don’t know if we can rule that one out. 🙂
I’d look for a verb that’s less ambiguous, and more explicitly about excelling. Citius altius fortius doesn’t include amplius “further”, but I’m thinking ὑπερβάλλω: yes, in Modern Greek that only means “to exaggerate”, but in Ancient Greek its primary meaning is “to shoot beyond [the target]”, and thus “to excel”, “to surpass”. So αἰὲν ὑπερβαλέειν “always to overshoot”. For some extra archaism, make like Germanic and do tmesis: ὑπὲρ αἰὲν βαλέειν “always to shoot over”.