Another option you might want to consider is asking

Another option you might want to consider is asking the tailor to use some of the fullness of the skirt to create another panel in the back. It looks in the photo like the skirt fabric is the same as the bodice fabric, just the other way up.
Brilliant! I assume that'd be something that can be inserted under each armpit, leaving the back zipper and the top mesh part and neckline (which fits well) intact.
This is a beautiful dress. I would look for someone that has a great reputation for making wedding dresses. They can insert fabric gussets at the sides or make a back laceup corset. See here: Adding gussets.
Pretty! Nthing that it's the same fabric as on the skirt, and taking out some of the fullness for another panel or gussets in the bodice wouldn't affect the look of the skirt too much (there's a LOT of fabric in a skirt as full as that).
Also seconding the tip to look for someone who makes wedding dresses. Look at their portfolio to get an idea of their sewing quality.
My regular tailor added 1" underarm gussets on each side from the the back of the skirt fabric for $20! Perfect. Now, any ideas how to accessorize it for an early 60s themed party? A nonthemed office Christmas party? I have a short red faux fur shrug, would that be appropriate at the 60s party?