Aeneid Translation Help

I have to translate lines 259 - 264 of Book II of The Aeneid as literally as possible. Lines 259-264 reads:

illos patefactus ad auras reddit equus laetique cavo se robore promunt Thessandrus Sthenelusque duces et dirus Ulixes demissum lapsi per funem Acamasque Thoasque Pelidesque Neoptolemus primusque Machaon et Menelaus et ipse doli fabricator Epeos

I translated it as:

The horse, having been lain open, gave those back to the air. And happily out of the oak itself they brought forth the leaders Theassandrus and Sthenlus and the dreadful Ulysses having been descended through a rope and Acamus and Thoas and Pelides and Neptolemus and noble Machaon and Menelaus and, the constructor himself, Epeos.

How much of my translation is right?

It will probably get you a passing mark. A few notes:

“Se promunt” is an example of the Latin middle voice, i.e. “They brought themselves out”, i.e. they weren’t brought forth by someone else.

You missed the sense of demissum in “lapsi demissum per funem”. Ditto for doli in “ipse doli fabricator”.

I think you’ve done all right otherwise.