Birdcage veil with hair down??

It sounds like by ‘traditional veil,’ you just mean that you don’t want there to be part of the ceremony where someone lifts a veil off your face? In some ways, I feel like that’s become so uncommon as to longer be what comes to mind when someone says traditional veil. (Though that could be different in your area.) If it’s just the veil concept in general that bugs you, I would probably forego the mid length veil attached to your hair. I think it would look nice, but, well, that’s pretty much exactly what Queen Victoria wore (along with a flower crown) and she’s my bench mark for the start of modern western wedding dress traditions. 😂

So to go back to your topic question on birdcages, this is the one picture I found that was more bohemian with long hair and a birdcage:

I think it looks pretty nice. What little you can see of her dress does not read retro to me, which is usually what you get with birdcages.

As kind of another thought, there’s something about your dress that feels a tiny bit renaissance to me. I mean, it’s obvious modern bohemian, but I was reminded of Juliet caps when I saw it. Admittedly, if you just try looking for a Juliet cap now, they’re almost all attached to long veils. But back in the fifties, they were usually separate headpieces, more based off historical lines. I don’t think the decoration on this works for your dress, but you might look at the concept:

This is a more modern interpretation:

Lace birdcage

Anyway, I hope you find something you like. And don’t worry— if the day of comes and whatever headpiece you have doesn’t feel right, you can take it off. Your dress will be fine without it, and I’m sure you’ll look beautiful.