Can Honey Be Added to the Syrup for Broken Phyllo Baklava Cake

I love the idea of the Broken Phyllo Baklava Cake and plan to try it.

The only thing that's throwing me is the lack of honey in a "baklava" cake. It seems like that could be introduced in the syrup but I'm also guessing the Milk Street chefs would have considered that. I didn't want to waste the time or ingredients if it's a bad idea. If it isn't already a bad idea, I'd also love some advice on the best way to incorporate honey into the recipe. I promise not to review it based on me messing it up ;-)

Thanks!