I suspect that you need to engage them more quickly. Can you advise on what to do about this?

Your assumption is correct. Only the zealots are placed in the corner for the battle, and the rest are single units, so as not to destroy the entire army. Also, due to the small army size, the dragons will be divided into several relatively small stacks, rather than standing in two groups of 250 units each. You can sacrifice 4-5 adepts for the "punishing strike" spell on the zealots. I don't remember very well right now, but I think you could equip a piece of Necropolis gear on the hero: the dragon won't be able to attack on the first turn. Then, cast "vampirism," and all the dragons will be eliminated, practically without any losses.
And as a general suggestion: it's better to practice on easier difficulties. If it doesn't work on "hero," you can also try on "recruit." The main thing is to get it right.