A long time ago, there was a tutorial on one of the truck forums where somebody did this. I tried searching a while back and found what I thought might've been the post, but all the pictures were gone and think there was nothing meaningful in the text. As I recall, the vinyl was slit circumferentially about where it changed from a vertical to horizontal surface. That vinyl was folded under the drop-in bin and fastened. The top was re-upholstered in a different textile because there simply wasn't enough vinyl to allow for overlap on both the top and bottom. Easier to re-upholster the lid, anyway.
I really don't think it's worth the work, and the parts are expensive..probably hard to get, anymore. Best bet would be to find a donor truck or take out that worthless center section and make a full-length console.
I guess you have vinyl seats, since I've never seen cloth seats without the storage. And I guess they're gray, since I've never seen any other color vinyl. If so, and you decide to try to mod the console to open,
Sutton Dark Slate Gray here is a source for the correct vinyl. If your truck is any other color or textile, I have no ideas beyond thse.