I love the original coat too OP. It's a pity it isn't in your size.
I don't understand why people are suggesting velvet (although I really, really, love the velvet orange one), or thin cashmere wraps etc. Maybe they didn't understand that you are not asking for an accessory for the dress, but a coat that will protect you and your dress from the rain, but still go well with your dress?
The burnt orange colour goes beautifully with the dress, and I think that you wearing the two together would look stunning. So if you can find a suitable coat in that colour, I think you should definitely go for it.
Would you mind showing us you ready for the wedding at the end of September please, you can leave your face out of the photo if you must...
Have fun - your post suggests that you are great fun after you have got over any initial shyness!