This sort of thing always has to decided according to context; my native language is not English, but perhaps using systematically expressions like "began to", "set out to" would make the English translation too heavy.
So he prayed there, the much-enduring goodly Odysseus, while the two strong mules bore the maiden to the city.
In this case, I don't think the first imperfect φέρεν is really inchoative; rather, it shows that the action of the mules is simultaneous with Odysseus' prayer. So its force is really brought out by
while. You could emphasize it even more by translating "while the mules
were bearing the maiden".
With the rest, I more or less agree with you. But again, I think this a question of choice – how much do you want emphasize the fact that the Greek has an inchoative imperfect (a beginning of an
effort – compare it to the inceptive aorist, which shows an instantaneous change of state, e.g. δακρύσας "bursting into tears"). You can never get every nuance into a translation, the translator has to decide what is most important in each individual case to keep the translation readable.
I think the newer revised Loeb translation is very good at bringing out this sort of nuance every time when it has some importance.