Bishop bag or slug tube is hanging there at the end of the hammock. One can put "stuff" in there for overnight storage out of the weather. Not as convenient as what you are looking at since the "stuff" ends up under the hammock at the end.
I would be looking at an open top box if I was trying to do what you want. Sides could be fabric and fold. Anchor point at the end to fasten to the end of the hammock with a bit of string. No sewing to the hammock body.
Free advice worth what you paid for it. ;-)