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If you are taking it in to be recovered, don't do anything else to it. Your upholster guy will be so much happier!
Bring him all the stuff, including whatever's left of the cover.
Even if it's gonna be a total custom re-do, there will be bits of it that he can refer to, as far as certain shapes for the proper fit.
Tell him what you want, he can tell you what's possible, according to your wallet & his capabilities.
If you're a rookie at this stuff, the upholstery guy's got the equipment & the expertise to do whatever, faster & cheaper for you in the long run.
I'm not trying to discourage you, but there have more than a few times where I've had to spend too much time undoing what a customer thought would be helping me.
The new cover will have 1/2" foam sewn into it. That's what's inside the sewn pleats.
There's a few ways to fill those scallops.
Fill them with what's called 'B-Felt'. Cheap, quick & easy. Like a raw cotton. It's that stuffing in old antique furniture. Think...'Chester's Used Car lot, Laundromat & Pin-Ball Emporium' cheap! It looks bad & will only get worse. You can do something similar with foam too. Same results!
Or, cut out each scallop all the same width so that they have square edges & a flat bottom. Cut foam strips just slightly wider & 2x as tall as the depth of the cut-outs. Glue those on three sides & stick them into the cutouts. Then cut them down level with the original foam height. Lotta work! Fussy, sticky work!
Or, cut off the whole top of the foam down to the level of the lowest part of the scallops. That'd probably be around 1.5"-2". Then I'd glue a new piece of new 2" foam back on, followed by some time shaping. This is the easiest to do in a shop because it needs to be done with the tools most upholstery guys should already have. I have some really long blades, electric foam cutters & I've made a specific tool just for cutting long wide thicknesses of foam using heated piano wire.
Doing it this way will result in the best job possible.
The new cover doesn't get glued down. At least, it's not what I would do. I've seen it done in other shops. Really no need in most cases.