What a lovely dress!
You could take the lacing out of the sleeves by unpicking the seams that hold the loops, taking the loops out, and re-sewing them. But that won't fix it if the sleeves are too tight over all.
I think if I wanted to change this as little as possible to get a dress out the other end that meets your standards, I would start by cutting the stitching which attaches the trim to the neckline and wrists, to free up the trim pieces. I'd then cut the sleeves off to leave short sleeves at a length I found flattering on myself. I would use the trim that came off the neckline to finish the sleeves, with a bit left over.
To fix the neckline, I'd start by unpicking the seams across the tops of the shoulders back a bit from the old neckline, and any other seams that went into the old neckline as well. I would unpick all the seams on the former sleeves that I'd cut off, to get pieces of donor fabric. I would piece the donor fabric back together to fill in the neckline, being very careful to get the seams symmetrical relative to the finished garment, and lining up the grain. Then I'd add the now-large-enough bits of donor fabric in to the neck hole, not worrying about how the garment won't have a good neckline just yet. I'd then pin the heck out of it so nothing moves and carefully join the donor fabric onto the dress body, folding all the raw edges under and into the space where there's 2 layers of fabric, so no raw edges are exposed to unravel later.
Then it'd be ready for me to trace a better neckline, and probably lengthen the shoulder seams as well since the new neckline will be narrower. I'd trace the neckline off a garment that I like the fit of, preferably one made from a similar fabric. I would go for a keyhole type neckline, with a vertical slit in the front to ensure that that the finished neck fits easily over the head. The trim that came off the wrists would be perfect for finishing that neck slit. Last, I would try to get the leftover trim attached to the now-smaller neck hole, but I would be prepared for it not to want to make a tight enough curve.
Some of the former arm lacing could be moved to the neck slit if you like the look of having that part lace up.
I would personally open the back seams with the lacing and add a bunch of the sleeve lacing into them, because I like the look of densely spaced lacing (like the current sleeve situation) better than the current back setup, but that's pure preference and you might have other views.
Now, if you want to make something other than a dress... it'd make a lovely purse or bag if you take all the trim off then put it back on strategically, or a cover for anything around the home that needs a cover, or a curtain (cotton/linen will fade in the sun worse than synthetics, though it's easy to re-dye, perhaps with natural materials). If you have any old items of similar fabric weight that are getting too worn to patch, you could use the old thing as a pattern to sew a copy of it from the newer fabric.