I'm playing Battle of Lake-Town, and I would like to know if the following strategy is legitimate:

I'm playing true solo and one of my heros is Beravor, and I am currently engaged with Smaug. I play Steed of the North on her:

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Response : After you engage an enemy, exhaust Steed of the North to ready attached hero.

I exhaust Beravor, and draw two cards. The quest phase begins, and I draw a new copy of Smaug from the Smaug deck, and put him into play engaged with me as per the rules:

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At the beginning of each quest phase, the first player must choose either his play area or the staging area as the destination for Smaug. He then reveals the top card of the Smaug deck and puts it into play in the chosen area. If he chooses his play area, he immediately engages Smaug.

In the next action window I then exhaust Steed of the North and ready Beravor and quest with her.

So what I am asking is: if I'm already engaged with Smaug, and and I choose to put the new copy of Smaug into my play area (replacing the old copy), do I count as having engaged Smaug again? The rules quoted above seem to suggest so.

That all looks good to me. 👍

Like you said, the rules say if you decide to put him into your play area he immediately engages you. I don't think already having a previous version in your play would negate this. Think of it as him flying off and then swooping down for another attack.