Hydrangeas get quite wide so it may look strange to have a -for example- 3 to 5 feet wide hydrangea growing only a foot away from the BOP. I am not familiar with the root system of the BOP or how wide it gets. If the roots grow mostly downwards, you could plant the hydrangea nearby and everyone would be happy and there would be little root competition for food/water between the two. Otherwise, you may need to place the hydrangea further away from the reach of the BOP roots.

Other than that, the area sounds fine for hydrangeas if you can provide enough moisture for the hydrangea. But not too much moisture for the BOP (the leaves turn yellow).

If, as you said, there is sun all around the shaded area, just little to no direct light, it should be fine. If your Bird of Paradise blooms, then you know you've got enough light for a hydrangea. Good luck digging it up.

Have you taken a look online at any hydrangea nurseries? There are a gazillion varieties and they're fun to shop for.